I never had problems. You are doing this in the Task Force screen?
Create New TG, Rename TG, Delete TG at the bottom left.
You can transfer ships from the 2nd tab from the left.
You should also be able to do it from the task group window, by changing the task force in the dropdown but it doesn't save your changes.
I've only ever bothered to do it in the Task Force screen(the one where you give your Task Groups orders...) It hasn't caused me any trouble.
You folks can bring that problem up as a bug on the Aurora forums.
I think we have a misunderstanding of which windows is which.
I'm saying that I can't change which Task Force my Task Groups are part of in the Task Group windows (the one where you can set orders, move individual ships between TG's etc.) I wasn't aware there was a way to do it in the Task Force window (the one that has info on the staff officers in the task force). In the Task Group window the dropdown menu doesn't save Task Force changes (at least for me). If there's a way to do it in the Task Force window, could you explain it to me, I just spent 5 minutes staring at that window and couldn't find one.
With regards to speed / weapons I'm a pretty firm believer in sacrificing speed for armory and armor. Sure, your 10,000 km/s ship might be super fast and hard to hit and with missiles you could outrange me, but at a similar tech level I could have a warship bristling with point defense and a bunch of long range weapons like laser/torps, or even my own missiles. Theres no point being able to zip around the place if that one missile launcher can't even get past my point defense or shields and the space and maintenance your spending on those diminishing returns engines is gonna pile up exponentially for every extra bit of speed you want while my weapons increase mass and maintenance at a predictable, linear rate.
Also, as far as speed as a defense goes, that is only going to be helpful against the first gen ships you meet from your enemy, at least with me, the second I see an enemy using stupid fast ships and hoping the speed will protect them, I shove all my lasers on 3x or 4x tracking speed turrets. Increases the cost and BP, sure, but it completely negates your defense.