Yup that cap goo is a sneaky problem. That's why the dishwashing method is 99.9% effective as it tends to get any goo you might miss by hand cleaning, or even submerging the entire board in an alcohol bath. Hopefully you got all of yours, because if any is left to fester it will ultimately corrode traces, and then you have bigger problem.
The soldering issue is exactly why I gave up on vintage computer collecting past the SE. I simply don't have the time or patience, nor the dedicated equipment to work with SMD caps (or any component for that matter), nor am I interested in taking it to that level. Thankfully, Mini vMac does just about anything the actual Classic can do, including boot from the embedded ROM System. If my Color Classic finally goes down, it will likely become an iPad stand or Mac Mini conversion project, simply because I love the form factor. My Classic II logic board has cap failure, so debating what to do with it.