"Been there, done that." The first several I made, I followed the instructions on the fusible interfacing and it took me days! but then I took a class and now this is what I do:
Skip using the damp cloth. Just use your iron and steam directly on the interfacing. If the interfacing starts separating from the t-shirt before you get it all sewn together, press it again. It will fuse again.
Don't be precise when cutting out the logo you want. Just roughly cut it out a lot larger than you want. I have found anyway that the squares shrink when the interfacing is applied.
Set up a wide makeshift ironing board, such as a piece of plywood (around 24 inches wide) with something covering it. Depending on the width of fusible, place one or two t-shirts right side down, put the interfacing down (making sure the fusible stuff is going to be fusing to the t-shirt not the iron. ask me why I say this.) and just start pressing with full steam, holding it in one spot for so many seconds like the fusible interfacing instructions tell you to do, overlapping, etc.
Just keep doing this until all shirts are fused, then cut apart and then do your final trimming.
I also went to the local lumber store and had them cut me a 14 1/2 inch square up from clear plexiglas that I use to cut out the block (I mainly do squares that are sashed together). My other square-ups with all the lines kept "making" me try to be perfect. Now I just use my clear square and "eyeball" it and when I think is is as centered as it can be, I use my rotary cutter to cut around the square.
This has saved me hours of standing at the ironing board. I first tried to be so precise and perfect and really when I saw some of the t-shirts I used. The print was so crooked or the shirt was so "well-loved" that who would really be able to tell that it is off center by 1/4 inch.
Hope this helps!