Undercooked center of a cheesecake baked at altitude
You should not need major adjustments to cook a cheesecake at high altitude. However, you are correct that the baking time may be slightly longer. The best way to account for this is to check for doneness with a thermometer: make sure the center reads 145°F. This is a fool-proof way to check the cheesecake is set, regardless of altitude, oven temperature, pan dimensions, or almost any other factor. This is further explained in a Serious Eats Article:

An instant-read digital thermometer is the easiest and most reliable way to test a cheesecake. Insert the probe into the very center of the cheesecake, to a depth of about two inches, and hold the thermometer as steady as you can while giving the readout time to stabilize. This cheesecake is done when it hits an internal temperature of 145°F (63°C), as carryover cooking will push it about 10° higher as it sits.

The primary mechanism by which a cheesecake &quot;cooks&quot; is the coagulation of eggs. Since this starts to occur at about 145°F, and your bain-marie will be at 195°F, it is plenty hot to set the cheesecake. It may take slightly longer than in my 212°F sea-level water bath, but it should suffice. (You could even cook at cheesecake in much colder water; see this Anova recipe that cooks it at 176°F using an immersion circulator.)
This Denver Post cooking column concurs: &quot;Cheesecakes do not need any altitude adjustments to the ingredients.&quot; Dever is at 5,280 feet, and they suggest baking an hour at 325°F. This might be a good place to start, but I would still use a thermometer.
Finally, it could be that your cheesecake it completely cooked, but not adequetly cooled. When you take it out of the oven, the middle should be slightly wobbly. It will further solidify as it cools. Be sure to cool completely for the best texture; overnight in the refrigerator would be perfect.