We had performance problems with Warptorio as we advanced further.
Although this may have been caused by using the Factorisimo mod.
But also because we use Bob's warfare and are able to stay on maps for a long time.
We've both disabled the Factorisimo mod and limited the size of worlds to 896x896.
However, now missions aren't spawning any more.
Could we have reduced the map size so much the missions are spawning out of bounds?
What map size should we use to both enable missions to work and reduce performance problems?

Yes... missions must have its range unlimited, or at lease 30 chunks ways... or more.
Press F5 and check the mod that is causing too muck ticks.

Thanks, we played another with the map size on 2500x2500.
If I'm correct each chunk is 32x32 squares.
So a range of 30 chunks is 30*32=960.
So we could easily reach the minimum range, any idea on the maximum range?

In this new game we did 2 missions, a third mission did spawn but we weren't ready at the time.
After that no more missions spawned, and we tried about 40 more worlds.

As for the performance problem, it seems Factorisimo caused about 1/4 of the tick time.
By far was Warptorio2 itself with about half, about 1/4 was due to squeak through.
The bad performance may have been caused by bad internet, because locally it ran much better.

Missions spawn if you have the technologies prerequisites already researched. if you do have it, it should happen. 40 more worlds is too much! are u waiting at least 4-5 mins each world ?
2500x2500 should be enougth. But I dont think map size is causing your lag problem... If you dont limit it, you will see no difference

Does this mean we shouldn't play Warptorio on an island map?

you shouldn't