Any suggestions on a waterproof mattress solution for my 94-year-old father who has chronic incontinence?

I would switch to a hospital bed or at least the mattress from a hospital bed.
They are cleanable, waterproof.
You can get a larger size hospital bed or mattress. Look for a mattress or a bed that is for bariatric patients. They are generally over sized.
If he is by himself a twin extra long (that is the size hospital beds typically are) will be much easier for the staff to make and as he needs more help they can raise and lower the bed so it is easier for him to get in and out.

MACinCT is pretty much spot on with my personal experience. I started with a really nice full size pad under the titted sheet but the pad was a pain to wash and dry. I picked up the fitted waterproof sheet at Walmart and it completely protects the mattress. I don't put anything above the regular fitted sheet. If it gets wet, it is easy to wash and dry and I just wipe down the waterproof sheet with a disinfectant wipe. Extra pads on top are just a nuscience and expense. If you are using incontinence under garmets, try to start with a dry one at bedtime. It will probably hold his nighttime incontinence and stretch out the interval between washing the regular fitted sheet.

I have used and bought in bulk the XL “Pet” potty training pads, it saved me from laundering bedding so often, and saved furniture.

Waterproof is not always waterproof.. i layer several waterproof ones to make sure it can't soak through. I have lots of them so I can layer new ones on while the others are in the wash. I also buy really good adult underwear. Northshore brand is the best I have found out there.. they don't link unless dad is being checked and taken care of properly.

My father was also incontinent. He wore diapers all the time. Sometimes he knew he had to use the bathroom. Sometimes he didn't. I purchased vinyl fitted sheets to cover the mattress and also placed a large mattress pad on top of the fabric fitted sheet directly under Dad to try to avoid accidents. Sometimes we were successful and sometimes not. I usually had to do laundry every day. One of Dad's caregivers gave me a tip to eliminate the urine smell on his sheets and clothing: Pour 1 cup of vinegar in the wash water. It works!

You can get waterproof mattress covers at Walmart. They can even be like a fitted sheet or a full zipped cover which I had to get my mom for MC. Next you purchase either disposable or washable pads on top of the bottom sheet

I used a waterproof mattress pad and every night had the aides put several chux on top of the fitted sheet. It usually worked. In the morning they just disposed of the chux..wet or dry.

We have a waterproof cover that zips around the entire mattress then disposable chucks, a fitted waterproof sheet, reusable incontinent bed pad. Regular fitted sheet two bed pads and either another fitted sheet or a top sheet (same color) to go over the pads because she “doesn’t like the look”. Before we got the aid we made layers of waterproof fitted sheet, fitted sheet, pads, same again and then again, the fitted sheets were different colors so one knew where the new fresh set started and you could just rip the wet set off and not have to make the bed each time. I don’t know how or if these systems would work in AL where different people are doing the work and I assume the laundry but maybe some version will help. I got everything on Amazon.

Confer with his PCP for equipment referrals. Look into what his insurance may pay for and hence getting a referral/ prescribed mattress from his PCP or appropriate home care equipment company may help towards this.
If you are receiving some home health care services for him,they should be able to make referral,options. If you do not have home health care services, confer with PCP about getting these services in the home to both help or and yourself going forward.

Incontinence is a constant battle. Be sure to test the waterproof mattress cover by pouting some water on it. For my Mom I use a waterproof mattress cover, then sheet, then large bath towel. Most of the time I only need to change the towel. I also put a pad in her diaper, or two diapers at once. I use one medium diaper, then put one large one over it. The only other method is to wake her up in the middle of the night to go to the bathroom. Good luck.