Your welcome, gooddog. You can't vent the heat and keep the dry air. You may want to try raising the humidity level. Hot and humid is unlikely in a basement. If you want to vent the utility room to the apartment, there are several choices. I just leave the utility room door open and blow the dehumidifier exhaust out the door. All other ways, done right, probably cost more money than buying an additional dehumidifier. The least expensive way to dehumidify the other part of your basement with a closed utility room is to add another dehumidifier. If that setup is unacceptable, the next choice is to vent your utility room into the larger part of the basement. This needs circulation both in and out of the utility room . If you have non-electric furnace or water heater in your utility room, you must ventilate in a way that does not cause negative pressure in that space (you can't just add one exhaust fan). If you have gas/oil burning appliances in the basement, you hopefully already have one or two carbon monoxide detectors on that level. The air needs to move both in and out a low at low volume. I'm assuming that the your utility room and the basement apartment share a common wall. First, I would investigate controlling the whole setup with a line voltage humidistat like the Honeywell H46C 1166. This device simply turns power on and off to humidifier and ventilation fans based on humidity. The honeywell would be placed in the apartment on the common wall. I haven't used this humidistat, but based on specs it would be my starting point. Most/all dehumidifiers save their setting during power failure. This allows these devices to be remotely controlled by simply cutting power. I'm assuming your dehumidifier has a continuous operation setting, and this setting is saved when power is cut. The choice for ventilation is one fan and a large vent, or two small fans running in opposite directions. The vent option would let more noise into the apartment. SInce these fans would run many hours per year, the most expensive fans provide the best economics. Panasonic 70 cfm through the wall fans are ~$170 each and very quite. The only issue is needing a finished looking vent cover on both sides. You could also investigate less expensive Suncourt products. People with wood stoves use these types of products to circulate air to adjoining rooms. You may think "spending this money, why not put in a whole house system in the ductwork". Expense aside, the problem with a whole house ducted system is dehumidifying the basement with the windows open upstairs. Running a central dehumidifier with the windows open is attempting to dehumidify the world. In a houses with basement humidity problems, the lower level needs its own system. In new construction a damper system could be installed in the main ductwork to only dehumidify the basement when the AC if off. But in new construction the correct approach is to adequately dampproof the outside of the foundation wall so that no special basement dehumidification is needed. It is worth listening to an HVAC company for their proposed solution based on your specific house, ductwork and climate. If running a second dehumidifier in the apartment is acceptable part of the day, an appliance timer could be used. Or an occupancy sensor could be used in a space to only run a dehumidifier when the space is empty.

I'm not getting into the vented vs sealed crawlspace pro & cons. but to answer OP's question, 3.5 to 4' is sufficient working room for spray foam install. closed cell has a stronger smell than open cell IMO. but the smell fades after a couple of days with either. if you are anyone in the family are sensitive then install should be done when ample time is allowed for any smells to dissipate. I'd start by investigating the recommended install (joists covered or exposed). I'd think that 4" would be ample at R-28, but I don't know your requirements in your area. just remember that you have to meet the code minimums. R-value of foam into inches of foam. not "performs like R-xx" or "average fill" same depth or MORE...not less everywhere. No Q or K values, R-values only. it is the installer that is the key figure in the install, not the salesman. make sure you are on page with the installer & be willing to go into the crawlspace & measure low spots before they leave for the day. it is worth your time. and yes dehumidifier in vented crawl is trying to dehumidify a portion of the great outdoors. best of luck.

3650 PSF is equal to 25 PSI..... Their dricore products are just massively overpriced, at least in the US they are. I think it is better to put down a foundation wrap (DMX), then 1" XPS foam (25-30 PSI). Assuming that the floor is flat, you could probably get away with putting flooring (with a membrane) directly on top of it. If your floor isn't flat, you probably will need a dedicated subfloor. I'd also be sure to use some kind of flooring that is somewhat rigid and install it perpendicular to the foam boards, so that if the foam boards do try to lift or sink, the flooring will add some rigidity to prevent it from mattering.

You need to check with your housing authority - they may have a minimum - R10 or R15. I'm in Minneapolis - zone 4 - I went with a total of R15. Installed top/bottom plate. Bottom plate pressure treated, with tar paper on basement floor - no direct contact with cement. I went with 1.5" x 48" wide XPS (pink stuff) against the wall - no studs yet (this makes a thermal break). Used PL300 to glue it to the wall - don't need a lot - one tube does 3 - 4 - 48" sheets. Then put 2x4's flat, 16" OC (you can get XPS scored 16", use a serrated bread knife to finish the cut), with 1.5" XPS between them - for a total of 3" XPS - R15. Take your time to make sure that the studs will fall in the center of the drywall joints. You may have to add additional 1x2's or 2x4's for the dry wall butt joints. Basement Insulation Basics Just an aside: my 1950's home had the old style basement windows. Replaced them with glass block - a lot more light once you get rid of the window frame and storm window. I found the glass block windows come pre-made. I ripped the windows out, including the frame. Installed the glass block windows with shims. Used a little foam to hold it in place. Next day, removed the shims, and foamed the rest of the opening. I framed around the window, before insulating, so I could do sheet rock 'returns'. Also what gives more light, is if you angle the bottom of the window 3" or 4" rather then make a right angle window sill.