Other than the orientation of the tip being different, I have difficulty to imagine why your “transformer iron” would be much better suited for desoldering 0603s. If there is any way that you could come up with a picture, “A picture is worth 1000 words.” OK; maybe 794 words. And yes these American soldering guns do put current directly through the tip. I think I had tried copper wire, but it did not work well and I was not patient with it. I suspect that using the correct gauge of wire can be very important. But thin wire will bend easily. I have some AWG12 = 2.05 mm wire. This wire is approved for electrical wiring in a home up to 20 Amps. If the 30 Amp number (current through the soldering tip) is correct, this does not sound like enough difference to bring the wire temperature up from (safety in the wall of a house) to (400 degrees C or so.) Also I suspect that the commercially available tips might use some alloy to get more resistance.
The key is to not switch it on for longer then about 3s as it got too hot.
I will also be not able to keep 0603 between two irons but you need only to pick it up and immediately switch gun off. After a (not noticeable) fraction of second 0603 is soldered to the gun. The tin is pushed out when the current flows and immediately pulled back in when the current is turned off. Perhaps the surface tension of the dissolved tin helps too.
Try to use standard iron (or even a pen) with your hand rotated 90 degree. There is only one comfortable position.
I use copper wire 1.4mm diameter. During using the tip gets thinner and thinner. If it is about 1.2mm then placed at PCB it will touch the capacitor at 0.6mm over PCB surface what in most cases allows to pick it up. Tip width (I have just measured it) is about 4mm. So when used vertically it can touch element (in a way that you can peak it up) 2mm over PCB what is certainly too high for 0603.
Original tips I got with it was made of 1mm wire (I think) and was curled up in two circles to form a tip.
When I said that I can’t imagine to use gun with vertically fixed tip I assumed that original tips are gone long ago and you have to use the wire. I never even thought of looking for original tips for my soldering iron and (thoughtlessly) assumed everyone else did as well.
May be your original tips are formed such that you can touch PCB with something really being a sharp tip (I just never had it in my hands). You can also form the wire to have the tip being horizontally bent but then it will be slightly weaker mechanically.
Thanks for your detailed information and photos. I have been working from home for many years, and some previous employers helped to supply my lab. For desoldering, I mostly use a desolder tweezer. At least for me, this seems to work better than anything else that I have tried. But your “transformer iron” looks pretty good. I doubt that that model was ever available in USA. I think that both your transformer iron and my soldering iron are from days when many countries produced their own products for domestic market.
And yes these American soldering guns do put current directly through the tip. I think I had tried copper wire, but it did not work well and I was not patient with it. I suspect that using the correct gauge of wire can be very important. But thin wire will bend easily. I have some AWG12 = 2.05 mm wire. This wire is approved for electrical wiring in a home up to 20 Amps. If the 30 Amp number (current through the soldering tip) is correct, this does not sound like enough difference to bring the wire temperature up from (safety in the wall of a house) to (400 degrees C or so.) Also I suspect that the commercially available tips might use some alloy to get more resistance.