Hi Beki, yes your vet is right really about not wanting to spay her until 5 months. Some vets will do it earlier but generally it is considered safer to wait until female buns are atleast 5 months so that they are strong enough to cope with the Op as it is quite an invasive Op for female buns.
Unfortunately, as she is both young and unspayed you are unlikely ever to achieve reliable litter training with her now. Some people get lucky, there is always an exception to the rule, but generally an unneutered rabbit of either sex, and particularly a young rabbit reaching adolescence, is going to be far too driven by hormones to be consistent in their latrine, as much of it will be marking territories and other hormone related behaviours.
I think that if she likes to use the 'sleepy' compartment mostly as her latrine then yeah, why not just put litter in there, or a tray, and move the bedding hay to the other part of the hutch for munching and dozing on for the time being so you waste less hay. Although perhaps a hay rack in the compartment would be a good idea so she can atleast begin to associate munching hay with being on the loo?
Don't forget when you bring her into your home, everything is new and unfamiliar and exciting and she's bound to want to mark it all with urine and droppings. I think you're just going to have to put up with it and hang on until she's spayed which I appreciate is annoying, although things could easily change at any time, her litter habits are unpredictable so could equally suddenly settle down, but I do think it is unlikely. I'm sure it will definitely settle down once she's been spayed. There is no reason not to persist with the litter training between now and then, it won't do any harm as long as you don't make it too much of a negative association, make the tray a fun place to be, yummy hay, treats etc. She may not catch on now but once spayed you can train her properly and any positive associations you make with the tray now should hopefully reinforce her litter habits for the future