There is no clear-cut answer here.

Is $1000 a fair price? Probably.
Is this something you can do yourself? Probably.
Is it going to be easy to do? Probably not.
Is dip stripping the best approach? Probably not.

I am not a big fan of dip stripping as it is not the best for the wood and joinery. You can use a paste stripper yourself and avoid the time and expense of removing glass. Removing 150 years of paint layers is going to take some time. And it will take time to remove it from the molding detail. On the positive side, if you are repainting, the stripping job does not need to be 100% perfect. Paint in the pores and nail holes can be left.

You'll probably need somewhere south of $100 for stripper, gloves, stripping tools, rags, and solvents, plus a long weekend to accomplish the job. If you have just moved into a 1850's vickie, you may have other jobs occupying your time.

Wait for a nice warm day where you can do this job outside in the shade.

About strippers

Stripping

Mostly, you'd be spending a lot of time. You'd need to set them up on sawhorses in an very well-ventilated area, (preferably outdoors), protect yourself with goggles and heavy rubber gloves, and resign yourself to several hours of cyclically applying highly caustic chemicals and scraping off toxic waste. It's not rocket science, but it is time consuming and unpleasant. Whether it's $1k worth of time and unpleasantness is rather subjective.

If you're planning to repaint them with an opaque finish, then you won't have to be quite as meticulous as you would if you intended to give them a clear finish.

Thank you so much for your responses. I think this is a job DH and I will tackle together at a later date. The reno should be done in a couple of months...we'll take a break and then start back on a weekend the weather will cooperate.

Neither of us have ever stripped paint before. It seems pretty straight forward, just lots of elbow grease. I am wondering how much of a nightmare that molding is going to be. There is no way of knowing how many layers are on these doors, but if I assume there are a lot, and I use a Methylene chloride stripper, how many applications should I expect? (roughly) I am not interested in getting it absolutely perfect, as I will be painting the doors an opaque color when finished.

thank you again for you help. Those two links were perfect.

MC tends to work "bottom up" and not "top down." Put some on and do not rush it. Rushing the removal, perhaps encouraged by the "works fast" directions on the can, you are substituting elbow grease and additional applications for just allowing the stuff to work. You can put a sheet of plastic over the top and that will prevent the MC from evaporating so quickly (if I recall, pure liquid MC has a boiling point of 87F) and allowing it to work. If you have to repeat the process, it's not the worst thing in the world, but dwell time is your friend.

I can also highly recommend the tool below for getting into the moldings.

Here is a link that might be useful: detail scraper

Another thing: do not be tempted to remove the old finish by sanding. This is very inefficient and will only lead to frustration. Also remember the possibility of any paint prior to 1978 containing lead that you do not want to make airborne.

Just a light sanding after you've stripped and dried the wood as a preparation to painting.

A decent brass brush is very useful for getting into molding with minimal damage.

Stiff stall brushes can damage the wood.
Molding scrappers can also be used, but the damage issue is even worse.

Use paint thinner to wipe down the surface and remove the wax used in the MC strippers to slow evaporation.

Methylene Chloride is very dangerous stuff.
It is not flammable, but is usually mixed with other flammable solvents.
When you absorb it (by breathing or skin contact) it binds to hemoglobin in the blood and ties up the oxygen carrying ability (similar to carbon monoxide).
It will slowly move off the hemoglobin, but if you have cardiac issues you can be in trouble with the reduction in oxygen transport it causes.

There are cartridge masks that can block it, but they are hot and often uncomfortable to wear.

Long sleeves, long pants, nitrile gloves (at least), and eye protection are all needed.
MC burns quickly if it gets on skin.

Working outside is a much preferred method, and a normal healthy person is very unlikely to have any problems.

The waste needs to be carefully packaged for disposal.
I usually use lots of newspapers to catch everything, allow it to dry over night, then bag up the residue.
It is likely to contain lead paint, since it was exterior woodwork.
Lead acetate (AKA 'sugar of lead') was used as a drier and gloss improver.

Wow you guys are great, thank you so much. We would do this outside, with the doors on sawhorses in the driveway, newspaper underneath to catch everything.

Yikes it sounds like scary stuff though - I am a healthy person, so if I take all the precautions, is this the product I should use? The other products didn't seem like they'd be strong enough. The doors are so caked with paint - lead based, I'm sure btw, it seemed like MC was the right one to go with.

My son removed paint from many doors and windows(many many layers) using heat. He did some research on the net and bought some kind of radiant heater off the store shelf for less than 50 bucks and modified it a bit and went to work. I am not sure it was radiant, seems like there is another type that has rods in it that put out a lot of heat. I helped him some and it worked pretty well. When the paint got pliable(hot) he used either a putty knife or wood chisel to remove the paint. It was far less mess than the goo type solvents and no dust. He found the heater method better than using a heat gun, however on your project you may want to try a gun to see what you think. Just another idea. Good luck

Why do you need to strip them to bare wood if you are going to repaint? The picture looks like the paint is not flacking. Why not invest in a few good sanders and just sand the current finish till it's nice and smooth. Then repaint. This is much less stress on the old wood and way less work. I agree with lots of the advise posted above but I would only go through all that stripping if I was going with a stained finish.

The paint isn't flaking but it is clearly caked, old areas that had chipped were just painted over and you can really tell. It's pretty gooped in the moldings. This picture probably doesn't accurately represent that.

I would like to put on a gloss or high gloss finish when done, which shows every single flaw. I don't need to get it perfect but can just sanding really get it prepared well enough for gloss paint? Especially in the moldings?

Well....this is promising. I'm over on the Old House Forum learning all about restoring my original wood windows. We will be building a steamer cabinet for our sashes, and it works on doors as well. When we build it, it will be so it can be taken apart in halves, so that I can use it on my doors, as done in this video, at the bottom of this page:

http://www.oldewindowrestorer.com/steamcabinet.html

Seems like it would be a LOT easier, and safer, and no chemicals. This is the method window restorers use that is the safest in terms of lead. (Wearing mask and gloves, of course.)

Has anyone tried this??