Looking at your original planting plan, it looks as though at least 1/2 of your plot will have veg that go out in late April, May and June ( Sweetcorn, French Beans, Summer squash etc.) so I think what I would do is perhaps cover at least half your plot with some sort of compost and then something over the top like weed control fabric or cardboard, this would encourage the worms to take the compost down into the soil and it could well be nice and crumbly when you take it off to do your sowing/planting in late Spring/ early summer, at least 2 or 3 months away.
Also, I think you are confusing the "average" last frost date with reality..... we are in Richmond, Surrey and I have had frosts in the middle of May on many occasions, losing courgettes, beans and getting the potato leaves burned by it, so please don't assume that there won't be frost in May where you are just because a website tells you that, it also depends on how open your site is and how protected a particular allotment is.