When I got back into it a few years ago I had a tough time with the lower back. The bike I picked up to rekindle the love affair didn't have a super agresive headtube (at around 140mm) but it came chopped for only 20mm of spacers under the stem. After rides I'd be pretty stiff and after tougher rides the glutes were firing pretty hard, and in my case the logical progresion of that is a back spasm involving the lower spinal erectors. In my case the chain of events initiates in the glute area, more specifically the piriformis.
I do not particularly care for the look of a flipped stem but more importantly getting back into racing even a little more aero helps alot. Stretching is much like training. Consistency is key. I found I didn't need too join yoga or spend hours a day strecthing but doing 4 or 5 different stretches within 30 minutes of getting off the bike helped immeasurably. My routine only takes about 10 minutes. Sometimes do it before the shower, sometimes after while on the floor infront of the TV. In one season went from a 4cm saddle/bar delta to 6cm. That's a big jump but I used to do a lot of martial arts and the muscle memory helped quite a bit.
I typically do a standing calf stretch, then change the intention very slightly and strech out the hip flexors, followed by a standing hamstring stretch, then lower back cat stretch, and the on yer back piriformis stretch. Also sitting cross legged and just leaning forward opens up the whole area for me. The KEY is not to go to far into the stretch to soon, breathe, feel the muscle let go and then repeat. There are many stretching modalities from dynamic, static, isometric and others. It's a deep discipline, with lots of different ways to crack the egg, each with it's advantages and shortcomings.
I also found tweaking saddle height played a role. Of course saddle height should be set relatively independant of most other factors but I found the teeny bit of leverage attained from a slightly higher saddle (we are only talking 1 or 2mm here) was negated by lower back discomfort after long hauls in the drops. Dropping the saddle just 2mm enabled me to hammer for longer. The .883 ratio that Guimard imposed on Lemond did not work at all for me. That's just my preference and it does take some time to get right - in my case it only took 25 years. Most folks reserve the drops for hammering. If looking to increase flexibility it's important to do a lot of Zone 2/3 miles in the drops. This really helps reduce the soreness after and helps the body ease into the new position. I would never drop the bars, not even a mm, if already in a building or peaking phase of my training.
When lowering the stem, if you are close to your own limit, do not go more than 2.5mm at a pop. Increasing stem/bar distance is much like increasing volume. Consitency and moderation are the big factors in success. If you want to go lower but flipping the stem is too low, a 0 degree rise stem as opposed to the traditional +/-6 (or whatever) is an option. Thompson, Colnago, and Easton have these stems available. The Easton stems faceplate attachment mechanism is [censored] IMO. I currently run with a Thomson.
Working on core strength with exercises like planks, etc helps a lot as well from a preventative standpoint.
That's for the time in the drops. For your knees you are on your own. When I was experimenting with position a little while back I did however find that when I was a couple mm's infront of the KOP (Knee over pedal) I would get a pain in the quads just above the knee, right around the medial head. Having ridden for so long in relatively the same position I just decided it was better for me to go back to KOP, the discomfort subsided immediately.
It takes a fair amount of time to raise FTP, it also takes a fair amount of time to get more flexible. Be patient, consistent, believe in the end result... one day it will happen.