I've done some Kolsch's and they start off slow. I did a direct pitch of 029 into the wort, no starter, took a little over a day to get going. About what I'd expect. It's not a fast starter in my experience, but once it gets going, not bad. I ferment mine at 60 degrees, which probably has something to do with how fast it gets going.
And yeah, no starter. Attended the BYO boot camp last march, attended a workshop put on by Chris White of White Labs. Yeah, that guy. He said unless he was doing a lager or a big beer, he'd just pitch the yeast, no starter. Well, you can imagine my head exploding when he said that. A couple people, when I mentioned this a while back, suggested he was just flogging his product, but I can't imagine he'd suggest that if it didn't work reasonably well.
So my son, who also brews, started doing that. No starter. He couldn't discern any difference in result. I brewed his Kolssch and decided to do that as well. Couldn't believe it. Fermented 029 at 60 degrees. I had that beer done and kegged in 10 days, force carbed it and brought it to my LHB club the next night--11 days after pitching. It was a hit, and nobody believed it was 11 days old AND I'd pitched that yeast without a starter.
Your slow takeoffs are consistent with my experience, but what you haven't told us is what temp you're fermenting at. Where are you with that? And how long is an "agonizingly slow" fermentation? With 029 I'd be at about 5 days after pitch and it's done. With Wyeast 2565, somewhat faster, but also no starter.
I don't think I'd be afraid to use your slurry a couple more times. Don't think I'd go more than maybe 5 generations with it.