Using pastry flour for standard sourdough bread recipe?
I have been making sourdough bread with a few kinds of flour. In my experience, bread flour (higher protein) really does make a difference in many qualities of bread that you look for -- texture, rise, chew, etc.  However it is incremental, maybe like 10-25% better, so it should still be possible to create good bread with lower protein flour.

I can give a few tips for your starter that I recently learned. The starter should be at least doubling if not tripling or quadrupling in volume each time you feed it. When I feed my starter I add 1/3 starter to 1/3 fresh flour and water.  So for example if I have 100g of starter, each time I feed it I take 33g of that starter (discard the other 67g) and add it to 33g of each flour and water.  After 2 or 3 of these feedings it at least triples in volume each time.  If it is sluggish, I make sure it is in a warm spot, ideally about 85F.  There can be a big difference in activity between this and a cool room temp of 65F.

Also the starter should be peaking in activity at the time it is added to the dough.  For me that's usually about 3-4 hours after feeding but it depends.  If it has fully deflated before you use it the activity will be less.

Something I have started doing is overnight fermentations of the dough, usually about 18 hours, at room temp.  This results in bread that is much more sour and has a wetter, stickier texture that I like, so might not be for everyone.  However it makes it easier to get a good rise. My dough will double or triple in volume overnight and there is not much harm in having it sit for a few more or less hours.  The activity and strength of the starter matters a bit less because it sits for so long.  When I'm ready to bake, I will "stretch and fold" the dough and it usually rises back up within an hour or two and is ready to bake.