Why is my topstitching puckering on the front panel?

The glue is your main suspect, not the needle. Contact cement stays slightly tacky for a long time, and as the panel feeds through, that tackiness drags against the throat plate and the foot so the leather hesitates between stitches. That hesitation is exactly what a wavy stitch line looks like. A size 18 needle is fine for bag panels, so I wouldn't chase that. And when you loosened the foot pressure, you let the leather slip instead of feed evenly, which is why the underside went loose. Put the pressure back to normal. The fix that saves you a rip-out: get the glue fully cured before you sew. Most contact cements want a good 24 hours, more if you laid it on thick. If it still grabs after that, a roller foot or even a teflon foot on that vintage machine will glide over the tacky spots where a plain foot sticks. They're cheap and fit most old machines. Also bump your stitch length up a notch. Short stitches on thick leather with glue underneath bunch up way faster than longer ones. Yes, sew the applique on first, before the panel gets glued into the bag body. Stitch the applique down flat on its own, then assemble. You'll have better access, you can see the feed, and you're not fighting layers of diferent thickness at once. If you've alredy glued the applique to the front panel but the panel itself isn't attached to the bag yet, you're probably still fine. Cure the glue, swap the foot, and re-stitch slowly. On speed, hand-wheel through the corners and any spot where the layers stack up. Don't ride the pedal and hope. A vintage machine without a walking foot will do decent leather work if you feed it patiently, but it won't forgive rushing. One more thing: vinyl thread can be temperamental on old machines. If the top thread keeps misbehaving after all that, swap to a regular heavy polyester and see if it calms down. Your wife's going to get a kick out of that bag either way.

Had the same wavy stitching problem on a wallet once and it turned out my scraps were the culprit, not the machine. I started running a test sandwich first, same leather layers glued the same way, and fiddled with that till the stitch line came out clean. Only then did I touch the actual bag. Saved me a lot of grief. Also, if the foot's still dragging after the glue cures, a strip of masking tape on the bottom of a regular foot can help it slide. Old trick, costs nothing. Curious what vintage machine you're on? Some of the old ones handle leather better than you'd think.

Seconding the advice to stitch the applique on its own first. When I did a satchel last year I fought the same bunching untill I started putting a strip of tissue paper under the panel while sewing, then tore it off after. The paper gives the feed dogs something to grip so the leather just rides along on top. Sounds fussy but it takes two minutes and it fixed my wavy lines completley. Cheap trick for a machine without a walking foot.

One thing I'd check is the moment the foot crosses onto the applique edge. That little step in thickness tilts the foot, the leather stops feeding for a beat, and you get a wobble right at the border even with everything else perfect. I must have sewn 30 or so panels on my old Singer before a guy at a repair shop handed me a hump jumper, that little wedge plaque, and my topstitch lines went clean overnight. You can also start your stitch line so the foot is already on the thick part, or shim the back of the foot with a folded scrap of the same leather as you come off the edge. Costs nothing to try before you touch the glue.

For me the culprit turned out to be the machine itself. My old machine did the same bunched-up stitching on a belt pouch and nothing I changed with glue or feet helped, until I ran my finger under the needle plate and felt a little burr on the hole edge. Years of one needle size had worn a groove and the leather was dragging over it every stitch. Swapped in a spare plate from a junker machine and the line came out clean first try. Check yours while you've got everything apart, cheap machines often have a beaten up plate sitting in them. Odd thing was it only showed on thick layered stuff.

Update: tried the tissue paper trick and the waviness mostly went away, so the feed dogs just needed something to bite. But now I'm seeing exactly what the foot-tilt person described, a little wobble right where the panel crosses onto the applique edge. Is the fix just slowing way down at that spot, or do people shim the back of the foot somehow?