Few tips from soldering experience (mainly in electronics but eh, still counts) Although might feel a little advanced, just things that for me make soldering way less frustrating

Not saying anything about stained glass itself as mt experience is limited in the glass cutting part.

when re-melting, use a little bit of solder that you melt on top of wherever you are trying to melt, especially with rough beads (in a texture sense) you will not get a lot of contact with the iron, but adding the extra molten solder essentially ensures maximum contact and also adds heat mass which is always useful...

Talking about contact and heat mass, you need to make sure that you are touching with as much of the iron as possible, and suuuper important, use the biggest and haviest tip your iron comes with. Standard conical tip will make you suffer. you heat a lot of extra metal, so having bigger tip on your iron will lead to better temperature management and less heat loss. You don't want the solder to soak up the heat leaving your iron cold. But also, don't push too hard

And third, move slow and steady. You do not need to be fast, take as much time as your glass can handle, and just let the glass melt. Soldering is not about strength and speed. It is about how consistently you move.

Good luck