laying 2nd, 3rd 4th..... courses

[Wozza]

Something like this..?

[oblertone]

The brick layer of your dome will be externally covered by insulation so don't worry about the gaps, just fill them with mortar rather than brick wedges. The internal face is where you need to concentrate on having small gaps, but without tapered bricks even this will be difficult. Save your cutting for making smaller bricks as the dome rises and you'll make perfectly good progress and archive a smooth internal dome.
If you are worried about keeping an even 'tilt' on your dome bricks you can pre-cut wooden wedges and reuse them as you lay a ring; you'll find you only need a half-dozen as the mortar goes off pretty quickly. Just back fill the gaps as you pull them out and you'll be fine.

[RandyJ]

I agree with the spacers. I used wire nuts for my spacers. The we're qwick easy and for me free. I agree I don't think I would do the little slivers I do not see good things from that.

Randy

[Wozza]

And having finished my dome I can say that filling the gaps on the internal of the dome with slivers of brick and home brew was the way to go. I trimmed the bricks from course 4 to course 6 (from memory), which was a real pain in the arse but you end up with relatively small gaps. Just using a small angle grinder it took me up to an hour to cut around 8 bricks.

I built a sand mould for the last three or four courses and however I cut the bricks there were still gaps, so you still need to squim yourself inside when you've finished and mortar them.

Those last few courses didn't really need spacers to hold them in place as the bricks were more vertical. The home brew did the job just fine. You do need more to fill the external gaps, but as someone said, the mortar isn't structural, it just holds the pieces together.