I have never "partially recapped" a board and then tested it. So I cannot speak from experience in that regard. But what I can say is that if you have the caps properly oriented on the board, and if the caps are good, and if you have not shorted anything while removing the old caps, then you should not blow a cap repeatedly like you have stated!
All tantalum caps and the two axial caps you see in
my SE/30 motherboard photo are from
trag. The photo clearly shows the white "+" silkscreen on the board and the proper orientation of the caps with respect to that marking. Note that the stripe on these yellow tantalum caps faces toward the white "+" on the board because that stripe indicates the Positive side of the cap. I must admit this is wickedly confusing for anyone who normally uses diodes because the stripe on the diode indicates just the opposite, the negative. But if all this makes you want to pull your hair out, just follow my photo.
I strongly recommend a DMM with "Continuity Check" for anyone who is not an expert with a soldering iron. I am an expert but even I have broken a pad or trace a few times in the past. And yes, I broke a couple pads off on my first attempt at a SE/30 logic board recap. What I did was put one probe of my DMM (Digital Multimeter) onto the thin stick of a trace that once connected to the pad, then I followed that trace with my eyes and tried to find another pad (e.g., IC pin hole) where it connects to. I then put my other probe on that, set the DMM to check continuity (which often makes a beeping sound when you have continuity). I then solder a very thin wire from that pad to my destination (i.e., to the place where I ripped off the other pad). If you've never used Continuity Check before, just set your DMM to that mode (sometimes marked with a diode and a little audi icon) and touch both DMM probes together. There should be a sound emitted. Some DMMs show something on screen rather than make a sound, but I prefer the one's that beep at you so your eyes don't have to be fixed on the DMM while you probe your board.
If you are really dexterous with the soldering iron, you could try another approach that avoids the need of soldering a little wire on the board. I have done this many times. You may need a magnifying glass to do it properly. Take an Xacto knife and scrape off the very topmost paint on the copper trace that used to be connected to the pad you broke off. Clean off about 5mm or so of that trace. Clean it until you see copper, otherwise solder will not stick to it. Then mount your cap, solder the other side (the side where you can apply solder to the board pad), then apply solder to the other side (where the pad is missing) but put enough solder on that side so that the cap pad will attach to the part of the trace you just cleaned. The result should be a tiny glob of solder on that missing-pad side, but it should not be a "mountain" of solder.
You can see an example of what I am talking about in
this SE/30 motherboard shot. Note the blue radial cap at board location I-11. You can see that the topmost foot of that cap is soldered to the pad on the board, but if you look closely the bottom foot had a broken pad so I used my "extension" technique to reattached it to the remaining trace. Since a rather large section of the trace was missing, I cut off a few millimeters of a resistor wire and used that to extend the cap lead to the residual part of the board trace. So in effect, I did use "a wire" but not one with insulation on it.
Even if you don't break any pads, you still should use a DMM with Continuity Check to verify all your wires after you remove the old caps. That's what I do. That way I know I've not inadvertently severed any traces or otherwise shorted something. Since I also have copies of the SE/30 logic board schematics, I can perform a very accurate and detailed check on all pertinent traces with my DMM.
Lastly, you have two choices when it comes to doing the two axial caps. You can completely remove the stock caps, which requires a lot of heat. (I could only accomplish it with a soldering iron that can go up to 450 degrees C.) I did that on my most recent board, which is shown in the first photo you saw in my post (the one with the yellow tantalum caps on it). Alternatively, you could snip off the existing axial caps and use the remaining stubs to connect your new caps. I did that on and older board
shown here. But that older board didn't look as beautiful to me. I am Steve Jobs with regard to board beauty, so I decided to "do it right" on my most recent recap job. But again, you cannot remove the stock caps without a very hot soldering iron due to some of the leads being connected to the ground plane (which is a lot of cooper that needs to be heated before the leg can be removed).
