Remember to water the begonias in the ground (no kidding, I keep forgetting). Count on 13 weeks from starting until flowering to be safe. I have found that keeping begonias indoors more than 6-8 weeks are difficult (they become too large)

Kenneth, thanks for reply.
Those time guidelines you provided are extremely helpfull.
Let me think out loud my plan and please correct me if I'm too agressive or plain wrong in my assumptions.

13 weeks from now brings us to the end of May-beginning of June, which would mean roughly 4 week of safe (frost free) growing outdoor from beginning of May. 13-4=9. That means that I should keep them 'frost protected' for 8-9 weeks i.e. whole March and April. In my particular case it's very doable: I could start them in square 4" or round 3 1/2" pots in my utility (65-70F warm, bright, but no direct sun light) room for 4-5 weeks. In April I could transfer them into unheated, but insulated storage room where even in a winter temperature rarely goes below 45F and stays in a 60's even in a hottest summers. Room is relatively dark, but I could keep fluorescent lights on 24/7 if necessary. At the same time I could start transfering some of them into 'to be a summer home' large containers similar to those on a pictures above, but still keep them in that room as I will not have a space restrictions there at that time.
Begonias destined to be 'in ground plants' could be replanted in larger (1-2G) pots as they would become too large.
Would it work?
I have an itchy fingers :-))
George