According to the 1955 edition of "Motor's Auto Repair Manual" the 1953-55 Kaisers with Hydramatic used a Delco-Remy 1107126 starter. It also states the 1953-55 Kaiser with standard transmission used a Delco-Remy 110725 so your friend is correct, they are different. Check the tag on the one you have.
Another problem that is often overlooked, and can cause hard starting, is battery cables with the incorrect gauge. Six volt systems used a 1 gauge wire where most 12 volt systems use a 2 gauge wire which is half the thickness. If someone replaced the cables due to corrosion, and replaced them with 2 gauge, you will experience hard starting. I always get 1 gauge cables at a tractor outlet near me, or if you want truly authentic cables, you can order them at
http://www.antiqueautobattery.com/But, check the number on the tag on the starter and see if it is a Delco-Remy 1107126 - if not, that's most likely your problem.