The pain that radiates from the glute region to the calves is most likely due to the fact the semimembranosus, semitendinosus, biceps femoris long head are innervated by L5/S1/S2 and the gastrocs are innervated by S1/S2. So when there is pain, the area you mentioned gets lit up.
The biceps femoris short head is also innervated by L5/S1/S2. I’m sure you feel discomfort here as well due to the innervation. However, it may be a minor player in this as it does not originate at the pelvis.
In case you forgot (and to those who don’t know), the other three muscles of the hamstring complex do originate at the pelvis - this is important.
As Alexus mentioned, it can’t hurt to look into the possibility of an anterior/superior tilt of the pelvis on that particular side. Too often strength/conditioning coaches, orthos, and pts falsely believe an anterior tilt of the pelvis is symmetric (that is, there is an even degree of tilt on both sides).
If you do suffer from an anterior/superior tilt, it may explain why stretching the hamstring complex provides only temporary relief. After all, you’ve done little to address the cause.
As for the hip flexor stretches, have you been consistent enough in doing them??? The psoas major is quite large. And we also have the psoas minor (a certain segment of the population do not) as well as the illiacus. If this area is the trouble spot, simply stretching may not be enough. A highly qualified person can manually work on the area.
A tight/overactive quadratus lumborum may cause superior tilt of the pelvis. Although issues with the QL, in my experience, generally manifests in some form of lower back pain. Something to put on the B list of possible offenders. If you do plan on getting soft tissue work done, proceed with caution as one of the insertion points is the 12th rib.
Based on the limited amount of information provided, these are some theories off the top of my head. You said you’ve suffered from this for several years. Therefore, it’s a safe bet that you’ve developed other dysfunctions along the kinetic chain.
As for the leg press you mentioned, I recommend staying away from them. Even if non-functional hypertrophy is your goal (nothing wrong with body building if that’s your thing), the problem with most leg press machines is that you never go into proper hip extension. This further promotes the shortened state of the hip flexors. Certain hack squat machines are a little better in terms of hip extension, but they have been known to cause knee irritation. And since your hamstring complex may not be firing properly (to help facilitate the lombard paradox), they may not be up to the task of getting you out of the hole.
Finally, I’m sure you know as well as I do that nsaids are not a long-term solution. And neither is popping fish oil (in case you were contemplating) like a kid popping M&Ms. In fact, many consider too much fish oil can put one at risk for muscle strains.