I think you’ll find most nursing homes don’t work this way. They either take Medicaid or they don’t. I don’t think you can “subsidize” Medicaid to get a “better place”? Maybe....but I don’t think so.
1) if a nursing home accepts Medicaid, once your in-laws assets have been drawn down to Medicaid levels (check your state laws for that level), Medicaid picks up the tab. What that amount is, is an agreement between the nursing home and Medicaid. You don’t “chip in more” to get a better room or better care at that facility.
2) if they don’t accept Medicaid, they don’t. Period. They don’t and won’t bill Medicaid. You pay the full amount and if you run out of assets you must move to a facility that does accept Medicaid.
In our experience (and as you saw) Type 2 facilities often cost less out of the gate because they DONT accept Medicaid. Type 1 facilities cost more, as private pay are making up some of the lost revenue from the Medicaid patients. Type 1 homes get much less from Medicaid than from private pay patients. But as someone else said....the care within that home is all the same.
The real questions are how many years do you think your in-laws could private pay? If you think they’ll outlive their money, are they prepared to move once they do? If not, then start with a place that takes Medicaid so they can stay when they run out.
In my mother’s case we opted for the less expensive place that didn’t take Medicaid, knowing she might have to move. We did this because 1) she had 7 years she could afford, 2) we felt she had about 7 years left (based on family history) and 3) she was suffering from dementia and the private pay home specialized in giving dementia patients a more “in-home” experience. It worked out extremely well and she passed away after 5 years, so we didn’t have to move her.