You could try an Elmer's Gluestick if you want to glue baste...they work really well and are pliable enough after they dry that pushing a needle through wouldn't be an issue.
Do you have your heart set on hand piecing? Or are you hand piecing because you think it will be easier than machine piecing? If you really WANT to hand piece, try finer pins...sometimes the big thick pins they try to pass off as "quilter's pins" at big box stores will shift your seams. You can find extra fine quilting pins from Nancy's Notions or another specialty catalog like that.
I personally think that machine piecing is easier...if you're trying to perfect your hand quilting skills I totally get it...but if you're thinking that hand piecing will be easier to start with I totally am from the school of thought that thinks it's easier to quilt on a machine to avoid what you're going through right now.
Just my two cents!!
Good luck, I hope you find something that works for you!!