@da9000
Some of these non-booting problems can be really tricky to solve, even with all the right equipment and knowledge.
If you're fairly sure it's related to a leaking battery, then as already mentioned, good approaches are to measure nearby vias and replace ICs which have been heavily corroded.
Don't let something else throw you off, such as a dodgy socket contact elsewhere on the board. If you haven't done so already, re-seat the socketed devices, particularly the CIAs. Socket contact problems there can also cause green screen.
If the battery has leaked significantly, it's highly likely to have damaged the U400/U450 (Paula/Denise) sockets. If the contacts appear green/blue instead of shiny, they need to be removed/replaced. Attempting to clean the sockets results in intermittent operation at best. Don't waste your time trying.
To remove the sockets, by far the easiest way and to risk the least PCB damage is to remove the pins one at a time.
Basically you do this:
1. Use a scriber/small knife to bend the outside most "leaf" of every contact sharply towards the centre of the socket.
2. Once every contact is bent away from the plastic edge, it helps to use small sidecuters to trip away the socket's thin plastic lip.
3. Arrange the board so it sits vertical, and one at a time, grip the contact leaft you bent inwards (I find low pressure on small sidecutters works best) while heating the contact on the solder side. Yeah, you need two hands for this, so don't try it if you're an amputee

4. After a few seconds of heating, the entire contact and leg will pull up out of the top of the plastic socket. Pull gently on the pin, it doesn't take much force to extract it once the solder has melted.
5. Repeat until all contacts are removed, the plastic body will just fall away by itself.
6. Clean all holes with vacuum desoldering tool/solder wick.
The only tricky part is the ground and VCC pins (2 or 3 of them on each device). Since they're soldered directly into the ground/VCC plane with no thermal relief, you need a *lot* of heat to melt the solder sufficiently.
Sounds time consuming and a lot of work, but once you get the hang of it, the entire operation only takes five minutes.
Assuming you've tested the ICs, clean any obvious corrosion from the legs and just solder directly into the PCB. If you insist on using one of those stupid sockets, at least use a decent machine pin one, and always use a new one.
It's near impossible to create a "bad" solder joint with plated through hole technology. Usually the worst thing you can do is have solder shorts, but you've got to be pretty bad to do that with component technology this big!
As for that isopropyl alcohol residue. I see that a lot as well, no idea what it is exactly, probably lead oxide from the solder. Don't worry about it too much, it appears to be inert and doesn't seem to cause any long term problems. Seems to be more cosmetic.
Hard to tell from your photo, but it does seem to be a bit worse than normal? You can brush it off if it bothers you.
Don't be too concerned about the purity of the IPA. If you're also using it in your crystal meth lab, then yeah, it needs to be pure :-) But for cleaning big chunky electronics, who cares? That's why pure IPA is hard to buy over the counter. At least here in NZ anyway.
Most of the time I just use methylated spirits (the purple stuff). Cheap, easy to get, and works just as well.
To answer your PCB questions:
The A3000 board is 4 layers. 95% of the tracking is all on the top and bottom (external layers). As you noted already, just about all of this is under the 68030.
Elsewhere, the internal layers are basically solid copper ground and +5V planes.
I don't have a copper mask of the board, but I'm fairly certain there is no internal tracking around the RTC area.
Tell-tale signs of internal tracking is often a via hole visible by itself with no tracks running out from it in one or both sides of the PCB.
This diagram shows PCB construction for the A4000, though the 3000 is much the same. It also shows how you can repair open circuit vias.
Hope that helps. I can say from a lot of experience that this kind of thing can sometimes be very time consuming and problematic to repair.
[Edit] Damn, that was a big post. Apologies if Wayne's server runs out of disk space, you can blame it on me :-)