I could never find a way to get the iron out of the way so the suction tip could seal before the solder starts to cool.
You're not supposed to get the iron out of the way. Leave it on the joint, put the sucker over the top, and press the button! A big chisel or bevel/hoof works well with a sucker. Silicone or the white plastic tips, it doesn't really matter; the tip will melt around the tip and form a seal.
A desoldering gun/station seems like it is the perfect medicine for batch rework of thru hole parts! So... how many people are still mass producing thru hole boards to screw up in the first place? For reworking prototypes, I can't imagine even allotting the space for a desoldering pump amidst the more important equipment.
Silicone tip helps a lot, but still when there is for example some big ground plane you could end up going back and forth with adding solder and removing it, just to get the hole cleaned, and the more you're there the higher the chances to make some damage to the PCB.
If you have a powerful iron and the right tips for the job, a good quality sucker will actually desolder anything a station can, just as well. There are some downsides. Probably the biggest is you need to use two hands. So you have to fix the board to the bench, somehow. I try to not add solder or flux to a joint I'm going to desolder. Better if you can get it done without doing so. Flux is what clogs these tools. And dry crusty solder will suck clean out the hole, just fine, if you can manage to get it hot enough and hit it with a good sucker. I learned this doing a batch rework job. The bevel tip made good nuff contact on the crusty lead free joints (crusty, like I couldn't even see the joint reflow), and the sucker did the rest. Took a bit of trial and error, but this saved a bunch of time cleaning the tool. Just take a few seconds to dump the solder bits every now and then; no gunk. Ran the tip bone dry, no wetting through hundreds of pins.
If you can't do a ground plane, you just need a bigger iron, lol.