As you well know, I am built in exactly the opposite way that you are. I am naturally strong but very tight - particularly in my hips and shoulders. (Thanks genetics!) After years of yoga I am finally starting to see teeny tiny steps towards opening, but for the most part, I'm still tight. Unsurprisingly, I tend to rely on my strength, all the while saying a little prayer that I'll wake up one day and my hips will have magically opened!
Early on in my practice, one of my teachers quoted Mr. Iyengar as saying that the first seven years that you practice yoga, you are opening up the hamstrings to prepare for the asana practice. (Interestingly enough, my google searches are not yielding results to confirm this quote so it may not check out.) Regardless, it's been burned into my brain ever since. You would think that this time frame would depress me. That the idea of something taking seven years to happen would leave me disheartened and weary. But it did just the opposite: it freed me from the daily waiting around.
If you took a phone book and tore one page out at a time, you would notice zero difference in the day to day. But over time, the phone book would start to dwindle in size. I think of this analogy often and know that each time I practice, it's one page in the phone book. Sure I have momentary lapses of impatience, for instance, seeing people in hanumanasana, a pose that seems like it was designed for another species. But for the most part, I try not to fret.
It isn't as though being able to bring my hands into reverse namaste would allow enlightment to ensue.... but then again, because of my tight shoulders, I couldn't say for sure....