LOL I have the same problem. My friend likes to launch missiles non-stop and then shoulder-tackle when I'm close. It's hard to close the gap without getting pummeled but I manage to come out on top. BARELY.
My Samus friend recently had a revelation. He calls me cheap for doing a desynched Ice Block approach, right? So he decides to launch missiles NON-****ING-STOP, shouldertackle through my sheild, run to the other side of FD and continue launching. My sheild can't take that kind of punishment so I figured I would try something else. I can't get the timing down yet because I'm not skilled enough but maybe you guys can test this out. The Climbers should be desynched.
As you guys know(or should know), The Parka twins' Dair cancels out a missile so I figured that by doing a desynched Dair approach, it may eliminate the threat of a missile spammer entirely! Basically, while doing the Block approach, if a missile is headed your way, have either Popo or Nana(whoever's turn it is to attack) short hop in front and Dair. If they continue, alternate accordingly. You'll gradually get closer(hopefully) unscathed and you can follow up with your own attack. As a side note, desynched Dair may also work with a wall as a psuedo-Drill shine infinite, since Dair's knockback is constant, no matter what %age.
Please note that I have NOT gotten the timing for this down so I'm not positively sure that it works. If one of you guys could test it out while I'm researching, it would be greatly appreciated.