Sorry so slow to respond had to review my data, I've been working on other projects.
Yes I would advise using the lpda to feed any center feed dish (not offset).
The lpda I used had a very high tolerance to focal point errors ,on most models there is a foot or more of "play" with very little change in gain or SWR in the ~470-695 MHz range.
It also exhibited a good SWR even when coupled to imperfect or even quasi-parabolic dishes.
I've yet to find a feed that gives better gain (on any dish).
One of its "weaknesses" is its pattern is taller than wider vs the biquads nearly perfect balloon shape.
So one could design a low wide dish that would favor the biquad some.
The model linked to above was an early model with lots of close horizontal wires (slow to run) it got 17.36 dBi net gain @ 521 MHZ with the biquad feed.
I made it 2 meters for convenience so 6.5 feet is a little less than your 7ft, but even wades 8 foot parabola only approaches the 20 dBi goal @ 521.
20 dBi is a pretty tall order at the lower frequencies.
I had never bothered to go back and put the lpda in front of that particular model (until last night) the lpda driven model gets 18.23 dbi net @ 521 MHz
You may be able to squeeze out that last 1.75 dB but...
If I remember right the first dish I saw get 20+ dBi that low was a 6 foot wide by 9 foot high square dish simplified to 12 flat panels.
The lpda I used was shamelessly borrowed from the 3rd post here
with pretty complete assembly directions here