So somewhere between 250 and 300 fish with about 1200 gallons of grow bed (very roughly). That translates to about 160 cubic ft of filtration if it all was wet. I know some of this you've already looked at and the fish stocking below is just there to give people an idea what the levels should be without having to look it up so here goes.
Here's the recommended stocking ratios from the basics thread - TCLynx post
MAX fish stocking per minimum grow bed/fish tank volumes
3 kg of fish per 100 liters of flood and drain media filled grow beds with 50-100 liters of fish tank
(1 lb of fish per 5 gallons of flood and drain media filled grow beds with 2.5-5 gallons of fish tank)
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Here's another yardstick from a post by Guitarwes
From what info I have gathered, safe stocking capacity in an average system could be from .63 lbs to 1.56 lbs of fish per cubic foot of wet gravel. This is total FINISHED weight of the fish and this is if you feed them at a rate of about 2% body weight per day as adult fish. This is if you have:
1) fish tank water exchange of 1 - 1.5X per hour.
2) adequate aeration
3) removing fish solids and uneaten food.
.63 lbs/cu ft is if you have only #1
.94 lbs/cu ft is #1 + #2
1.56 lbs/cu ft is #1 + #2 + #3
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Usually to avoid cleaning the grow beds I suggest stocking lightly which you really won't be doing. The worms will help break down the solids and make them more available to the plants but they won't remove all the solids and you will eventually have to clean the grow beds. You could use a pre-filter and create a bypass loop for when you have to go on vacation and don't want to mess with cleaning the pre-filter. That's probably what I would do in your situation. The pre-filter would probably remove between 30 to 50 percent of the solids and would, at the least, extend the time between cleanings, in return for regularly cleaning the pre-filter.
You could also set up the grow beds to allow diverting the flow out of the system and then quickly pour a couple of 5 gallon buckets into each grow bed so the solids flush out - Do this while the beds already have water in them - this would work best with the expanded clay pellets that can float. It isn't perfect because some solids might still get caught at the media guard but it's fast and easy. Take you maybe 5 to 20 minutes per bed, mostly filling the buckets. I'd probably do it one bed each day over a period of several days. RobBob on YouTube has a video showing another method which is better (it gets roots and larger solids).
I'm not sure how long you'll be able to go without cleaning. A lot depends on the size of the fish and how big you intend to grow them out. You've got a pretty good size grow bed filter already but Tilapia eat a lot so

. Personally I'd at least leave the space to add a filter if you need to but just run with it for now and see if you're satisfied with how the solids build up looks.
I have a feeling that part of this depends on a persons tolerance for having solids in the grow bed, mine is relatively high as long as they don't get disturbed or aren't clogging up the bed. Think of it as rich flood plain soil. I run pretty light fish loads though and I think that makes a big difference. I'll run about 40 fish (bluegill or channel catfish, more BG than CF) with 400 gallons of grow bed and 1100 gallons of water running through the system. I haven't had to clean the beds since I started this system 3 or 4 years ago. A good portion of the year, water temps are cool (below 50) here so feeding is light to non-existent. Having said all of this, I am planning on adding a solids filter because I'm connecting up a DWC setup and I plan on increasing my fish loads. Probably be using a homemade static media filter (with Kaldness media) as opposed to the RFF. I'm hoping to eventually drain the solids out to some fruit trees.
Hope you get something you can use out of this
Cheers