Hi Creagan, whereabouts are you? North Scotland somewhere?
My soil sounds similar to yours, thin over rock, except we have pockets of deeper volcanic soil in places, which is where we grow our vegs.
In the past I have always grown in the ground, but this year we have made 6 x 1mx2m raised beds inside our polyttunnel, using scaffold boards (9" deep) for the sides. To fill these I bought 2 x tonne sacks of mushroom compost from a farm about 50 miles away - the 2 bags fitted into the sheep trailer perfectly (delivery charges were high.) Is there anywhere within striking distance of yours which sells mushroom compost? The 2 bags were not enough to fill 6 beds, so we used molehill soil (plenty of that!), our own FYM, and old bags of multipurpose compost as well.
I like the lazy beds idea for the tatties, as they do need deepish soil. Do you have any livestock bedding you can use for bulk? Tatties are quite forgiving about the freshness of manure. Definitely don't waste your precious compost on them! You could use your slimey grass clippings mixed in to the tattie bed, and for the rest of the year add a bout a 2" layer whenever it's available. It will dry before it rots if we have sun and will help to keep the light off and the weeds down.
If your compost is well broken down, mix that with the soil, seived if you can, for the carrots, plus some sand unless your soil is already sandy.
Peas and beans like
fairly rich soil, and leeks and brassicas such as kale and sprouting broccoli like
very rich soil so need FYM.
I envy you your access to seaweed - we are slap bang in the middle of the south of Scotland, about as far from the sea as we can get
. You can use it anywhere, so be generous but of course it rots down to little bulk. Is there anything else you have in your environment to help fill the beds?
Don't make your beds more than 4 feet wide as you end up standing on the soil. We are finding 3 feet is wide enough. Don't expect your beds to be perfect in their first year - it takes a few seasons to develop their fertility, by adding more compost or FYM on the top and letting the earthworms work it in for you.
Good luck with your new veg project