A tip I picked up somewhere - take your clippers and cut the top corner of the blade off to make it pointy. It's a lot easier to get it into the holes that way.
The guy who taught me pointed out that you can bend a scrollsaw blade to the side just about as much as you want. It's the front/back bends that kill it. Obviously you can't make a sharp bend, but they are pretty flexible to the side. I also find good light helps a lot. I carry a little tactical flashlight and I often wind up setting it on the saw lighting the bottom of the wood when I'm trying to come up through a hole.
When you look at upgrading your saw you might want to look at a Jet. Not cheap, but worth it. They use a lower blade holder that's really easy to use. Comes with three (I keep different types of blade in each one) and you can get more on Amazon. The table has a slot almost to the front edge so you can, if you need to, pop the blade holder out of the lower arm, bring it to the front of the table, come up through your hole, and then slide the whole thing back into place. Lower holder is very easy to put in place and the top is a flip lever that locks and tightens the blade.
Important note: on a Jet you do NOT set the tension with the knob at the back of the arm. It's just for getting the arms parallel. It does have some effect on the tension, but it's way crude. You set the tension by rotating the lever. Clamp the blade, check your tension. If too loose, open the lever, spin it around one turn and try again. Once you get it set, it's set. Oh - put a mark on that back knob so you know if it has turned itself while the lever was open. I use a bit of tape. I'll occasionally see it having turned a bit. One time it was a whole quarter turn off position. Another tip I got here.