I had the same problem. Had old strip flooring that was over 100 yrs old. At one point someone replaced a section with 3/4 thick wood floor but you wouldnt know until it was tore up. When I laid all the flooring an got to the the hallway I was up about 1/2 in. I shimmed up an 1/8 in then stripped a blank of the new floor on the table saw to build a thin transition piece. There is a slight raise but everything is the same level and looks nice. So in short just use a reducer.

My concern is the layers of vinyl underneath the hardwood. Hardwood doesn't like sitting on vinyl and vinyl doesn't like sitting on hardwood. The two do NOT like each other. If you think this is a good idea (which it is considered on the technical side of things a horrible approach to this) then you might have to add another layer of subfloor. A nice, fat, thick 1/2" plywood to cover those two layers of vinyl. Now you can go ahead and lay the hardwood. Technically, my suggestion is hideous. It is atrocious. It is so "unprofessional" that I could weep. But if you insist on leaving the vinyl in place, then you need to think of a way to separate the vinyl from the hardwood sitting on top....and one very sure way is with plywood. Again, my suggestion is a travesty. Then again so is laying hardwood over two layers of vinyl. In the flooring world, we 'allow' ONE layer of resistant flooring (like vinyl) to sit underneath another floor. For example: the first layer of vinyl was considered "OK" to lay another layer of vinyl over top. All good. No one in the technical department batted an eye. If a THIRD vinyl floor was proposed (or a laminate, or linoleum, or cork, or hardwood, or tile, or even carpet) it would be a "NOOOOOOOO! STOOOOOP! DON'T DO IT!" type of answer. So I will officially say: No. Stop. Don't do it. There. It has been said. That being said, if you as the homeowner choose to forgo the installation instructions and the "Best Practices" as set out by the National Wood Flooring Association (as homeowners your word is "law" when it comes to things like this), you are welcome to go ahead and lay hardwood over two layers of vinyl. If you do it, I suggest a new layer of plywood to help things along - because you need FLAT. And most "old hardwoods with two layers of vinyl sitting on them" are anything but flat. Good luck. You would be better off remediating the asbestos/vinyl and getting down to bare hardwood. Now a new floor (with the help of a layer of plywood) can go down. Or you remove the original hardwood with the vinyl (this is easier to do than scrape off the vinyl...and easier = cheaper) and start with a new layer of subfloor and go after it like it should be done. But as homeowner your word is "law". If you tell a professional to "just do it", they will say "yes ma'am/sir" and do it. But they will not warranty their work. You will be left holding the bag - and all the pit vipers that lay inside. It's your call.

Those "gaps" are mild. They are normal. They are expected. They tell the story that they are original. They are meant to be there. The new floors will eventually do that too...which means they will match (eventually). It might take a decade...but it will happen. And don't forget that once everything is sanded down, you will be VERY surprised at how those "gaps" seem to go away (visually). Why, you ask? Because some of that is dirt. Once the floor has been sanded down (1-2mm of wood is taken off with the sanding), the dark material between the planks gets shaved off as well. And voila...they look cleaner (because they are). Relax about the absolutely normal spacing between planks. Unless you have museum quality climate control, this LITTLE bit of shrinkage is normal and to be expected with every floor (especially if it is 30 years old).

Thanks SJ McCarthy! Given what you said about the original floor (oil based finish - I think they are Swedish finish from what I one time heard from the listing agent - and no stain), what would be a good selection for factory pre-finished floor? The purpose is to lay down the new floor for now in the carpeted area and make sure they don't look too different or visually unacceptable. You also mentioned that the natural break (doorways and breezeways) will help my change, which I assume it means the natural breaks will make the mismatch between floor area less obvious. I think they are plainsawn from the pattern, red oak, so going for something like a natural red oak from say Bruce with same strip width would be OK? Or what color would be best to match the Swedish stain? I take what you said "Even a factory finished solid red oak floor can be refinished like the floors you already have. It makes it easier in the future to get them all the same colour/finish." as that I can refinish everything in the future (e.g. 15 years down the road) to get them all aligned in finish and color if I want to. I am also planning to install the hardwood floor in second floor. Since they are at different floors, do I better off use the same species/stain/finish of wood for second floor? If so, can I go with a wider plank (say 3 1/4" or 5")?