The advices that I provided allow you to troubleshoot by elimination. You however seem to be inclined to troubleshoot by guesstimating. You logic is up to you, but just so you know how strange it sounds to a uneducated and shortsighted person like me, let me show you my logic.
" everyone says they only have this problem with my Skype calls, nobody else's, so that kinda suggests the problem is my end to me" -people's opinion is subjective, and the test with another iPad on the same network or with the same iPad on better network would be more precise. Even without that test, nothing points that the problem is with your iPad or network, nor does it allow you to establish which one of those two is the culprit.
"The signal strength is excellent, no problem there" That is just sooo **** funny, since the signal strength or speed of your router is not the weakest link of the Internet, speed of you ISP is, and especially upload speed. Our even outdated routers, would still be 25 times faster then my home Internet. And you just confirmed all that by your next paragraph "I occasionally get the can't connect to Internet message when the signal is full strength".
I have no idea what is going on either, but you asked for advise and I attempted to provide with steps to understand, whether you decide to use those is up to you.