Matt, I would water spray Weed-B-Gon. You do want to do this when you are not expecting rain (or snow) for a while, also while the wind isn't blowing so hard that it's tough to control the spray, but it does a great job.
Crab grass is tough to kill once it has woken up from the winter. You pretty much have to get that before the Forsythia bloom--or about the same time. Past that, you have to dig it out.
The problem with many fertilizers is that they are just heavy nitrogen with not much else. Nitrogen gives the top of the grass a blast of food/energy but the roots don't get much out of it and so it doesn't last. As you apparently know, if you put too much on, the nitrogen burns the lawn but it generally comes back strong later. The burning can get the weeds going good. With high nitrogen fertilizers, it's a lot safer to spread at half the recommended rate or less.