If I remember correctly in custom event you don't have yuor career engineers available, but in Career or Custom Championship you do and with them cars can be repaired more. Custom Championship is more practical playmode to do it because you can retire events without level drop which happens in Career when u place 14-16th in total points at the end of the season.

All though in those playmodes time of day and weather conditions can't be chosen(it's randomized) but the ability to fix the car more can result in quicker time (specially in Finland where cars tend to get more damage). Weather conditions doesn't affect times in Greece because there's no rain, in Finland it's like couple seconds on a long stage and Wales stages are always wet, not much difference if at all in cloudy/overcast or rain conditions. Night stages shouldn't affect times that much when u know stages.

So is it allowed to do 12 stage RTA through the Career or Custom Championship?

Sure but you can't exactly choose the event or stages you wanna do.

Ive had times I wanted to do a Finland and the game kept giving me four straight Greeces lol.

When you do Custom Championship u can choose all 6 events 12 stages per event. Twelve stage events will have all the stages driven once.

If u get Greece first just reset timer, start the 1st stage, pause and choose retire from the event. When u see option to continue to next event then start timer again at that point and next one might be Finland. If it isn't again just reset timer, start 1st stage->pause->retire and so on until u get to the location u want to do.

You won't able do any proper splits because order of the stages is quite random. Maybe keep a list of your individual stage times in custom event speedrun available to see if it's worth to continue run after certain amount of mistakes/time losses.

I think Finland might be only location where you actually could gain time from career engineers and specially if you're driving Group A/F2 Kit Car/R4/2000s/2010s class cars. Those more modern cars are more complicated and require skilled engineers to get them fixed.