The solution to all these problems with raised beds is to dig out the paths down to the subsoil and fill the resulting trench with woodchip. The topsoil from the trenches (which was being wasted and ruined by pressure underfoot) can raise the beds further improving drainage.
This is not theory - this is 5 years of experience - all entirely positive.
There is no problem with nitrogen 'theft' because the woodchip is not distributed through the soil - the growing soil is completely separate and there's no way the 'thievery' can move more than a few mm into the boundary. Crop roots will multiply where the nutrients are (in the bed soil) and just won't bother going into the paths.
Weeds in the path aren't a problem because they are unbelievably easy to pull out of deep woodchip - in fact I regard the paths as weed lures for rampant perennials - couch prefers to run through the woodchip (the desire for expansion seems to outweigh the desire for rich soil) but when any weeds appear I can lift them in a tenth of the time I would waste if they were in the soil. Many weeds can't resist a nice loose medium - and they never learn.
Admittedly my heavy clay soil makes the fatal choice easy for them, but if you're on light loam you don't have a problem in the first place (even if you think you do) you won't have any idea how bad these weeds can be.
As the woodchip turns into humus the level can go down quite quickly, especially at first, but you must keep topping them up because if the level drops below the bottom of the boards then soil will wash out into the woodchip and that would stop it being such a poison chalice for weeds.
Personally I'm looking forward to having a 30cm deep layer of humus in a few more years time because then I can use it as mulch and start again with fresh woodchip (adding cheap nitrogen helps speed the whole process up - I would recommend free liquid home nitrogen).
Cheers.