I bought a pack of Dahlia tubers at walmart, they didn't look very good, but I went ahead and planted them anyway.. there were three altogether, but two of them were all falling apart.. BUT, they are starting to come up.. one is up about 3-4 inches, another is just peeking thru and I have yet to see the other one yet. I put them all in the same pot, a large container cause I wasn't sure if they would even do anything.. and if they do well, I can alway separate them.. will keep you posted.. they are going to be gorgeous if/when they bloom.. I don't remember the name, but they have beautiful red petals and yellow centers...
I live in Ohio and also have clay.. grrr.. it is a pain in the rear to say the least.. I do alot of container planting and that stuff that I put in the ground, I just dig the whole about 3 times as big as it needs to be and then fill in the rest with potting soil/top soil/sand/manure mixture.. and they do great after that.. I mark where I put my stuff in the ground, even the annuals, that way I know where the 'good' soil is for the next year!!!
I would think if they are very root bound, you could transplant them with no problems... even if they are in bloom. Can you dump the whole plant out in the palm of your hand so you can see the roots? You would be able to tell better by doing that just how many roots you have... And like Wrennie, I am not sure how badly a plant has to be root bound before it starts to affect them.. but if it is very bad, it probably won't grow as much, like you said.. and it may hinder it from producing new blooms.. not sure. Good luck though.. and keep us posted.
If you are unsure of the need to transplant, can you get a picture of the roots and post it here for others to judge maybe.. I dunno. ;)