Interesting, I talked to an instructor at another LDS. He told me that a surf exit with gear on isn't a requirement on any dive in the OW program. But in my mind a crab crawl on the first dive would be a good idea, so that everyone is on the same page.
Yes not a requirement but usually is the best option, dropping your gear in the surf or the sand unless somebody else is carrying for you "usually me" is no less strenuous and sand will get in everything and you will have issues "and I fix" I think it easier to walk out with it on your back. As for crawling out or a rough surf exit we call it the "Monastery Crawl" those who shore dive Monterey/Carmel know why is not easy either it is a tool for getting out when it is rough we have our students do it on the first dive at the ocean. Private instruction may be the best option for you because you are paying for the service and can set the pace. This has been a bad few months for classes due to ocean conditions so lots of shops are backed up on cert dives so they may not be able to get you in earlier because those students are catching up as well and were ahead of you the ocean does what it wants and you have to go with it. You had a chance to finish and you called it and that's fine there may have been some options to renting another suit from Breakwater Scuba its like $13 a day we've done it, regulators have had a local shop lone one to us etc. don't condemn your shop because you decided to call it.