Green manure headache!

this is what has always put me off green manures.
the principal is good, but there is no way I could dig in.
sorry I cant give any decent advice.

There shouldn't be much of a  regrowth problem if they didn't flower, but it might still take a long time to rot down.

I've used green manures for years and never had problems. Wouldn't be without them, but timing is important. I do  make sure however I avoid the deep rooting sort like alfalfa and grazing rye and do the 6 to 8 week buckwheat/vetches/field beans  etc for green mass vegetation, top 6 inch structure, some root and nitrogen. Broadcast works far better for weeds than rows. A lot of people do short stints with alfalfa and dig in before the winter sets in to avoid the very problems you've had.
Breaking down hard clay pans seems a bit far fetched and I wonder if those sort of manures are more suited for larger scale mechanised farming rather than our needs. If it were me with that hard clay, I think I would go down the lasagna mulching/composting route.

I never understood to attraction of a green manure, especially a grass based one. People spend lots of time digging over and removing grass from their plots, then the recommendation is sow a grass on it and dig it in once it has established itself.

I know the principle behind it just never was sure if the result was worth the final effort.

I use Italian rye grass and do the following.
Sow in September or earlier if empty soil. Cut down growth 2/3 times and leave it lying, cover the growth completely with black plastic in November. Cover the edges of the plastic with soil to exclude light and I use water filled milk cartons to weigh down the middle.
I uncovered a bed yesterday and just needed to lightly fork it over. Lots of worms in there and the mass of fine roots rot down to add bulk.
Works well for me. I have tried other green manures but just use this now.

I've grown Hungarian Grazing Rye over-winter for some 12-15 years now. I have a total of 4.5 ten-pole plots, but 2.5 of those are given over to fruit in one form or another. Of the remaining 2 ten-pole plots, some 12 poles or so tend to be sown with grazing rye during the autumn. I find it tends to be about 2 inches high within 10 days of sowing, about 8 inches high and green and bushy by Christmas, when it pauses, then grows on rapidly from about now.
As I have a large-ish area, and am getting on in years and have back and knee problems, I resort to machinery rather frequently. I tend to either strim it to ground level, or mow it with a petrol hover mower, leave it for a few days, then rotavate it in. Particularly if you hover-mow it, it seems to disappear, but I figure it can't have done, the same biomass must still be there, just ground into finer particles so you can't see it so readily. And it's already done its over-winter job of reducing weeds and minimising water run-off / leaching.
Ideally you won't sow small seeds into the soil for a few weeks, as the grazing rye has an inhibitor that reduces germination until it breaks down.
Another thing I tend to do, not really recommended unless you're a sad old person like me with time on his hands and the need for soothing repetitive therapy, is allow a proportion of my grazing rye to grow on to maturity. It gets around 6 feet high, with seed heads as long as your longest finger. As I haven't yet devised a more efficient method of harvesting these, I pluck them one by one, perhaps eventually filling a big rectangular recycling box. I re-sow these in the autumn, thus saving a small amount of money, but gaining an amount of perverse satisfaction.
I also use free horse manure on other areas of my plots, but find that broadcasting a few light bags of rye seed much less wearing on my back and limbs than shifting many hundredweights of animal manure!