Hi there!
In my profession, I advocate for families for these kinds of services and second the notion of pushing back on school to increase to at least 45 minutes per day. They'll definitely argue that this will cut into his school time, which puts a strain on whatever their progress goals are, but let them know that YOU have progress goals for your child as well.
You may also want to look into OTA's, Occupational Therapy Assistants. Often they can work with monthly or weekly supervision from an OT or a related therapist (depending on the setting). You may also find that bulking up BIG TIME on the homework from the shorter or once a month OT sessions will give you lots of at-home materials to work with.
With these materials, you may be able to hire someone outside of a formal therapist, say a QMHPP, QMHP, PTA, or even an early childhood education student (maybe a TA at your son's school?) who needs a side hustle/extra income. Interviewing and finding the right person for say, $15/hr or so 1-2x per week could give your child more hands-on time to work through what has been assigned in formal OT, but at your home or at a local library.
I can't stress how impactful I have found it to be for families to seek outside help for special tutoring/OT/PT/ST/ABA/etc. It can really help generalize skills across modalities, people, and places for a child to work with others. I always give the example of my very intelligent mother trying to teach me Algebra ... No matter what she said, regardless of her brilliance or commitment, I was unable to learn Algebra until I got an outside tutor that I clicked with (the neighbors daughter, actually, so still fairly frugal of a choice)... and it made all of the difference. This was not a failure on my mother's part at all, it just opened up my options.
Good luck! You can do it!
*also, if you feel like your school is going beyond being "difficult" during IEP reviews or meetings (like bullying you), you can reach out for a county or school system student advocate, which is generally paid through a waiver (although this is VERY different state-by-state and even city-by-city). They will/may attend meetings with you (or call the school) and push back through a more legal and policy-based lens than many parents are able to (not a dig on parents, just trying to explain this as best I can).