Well, for a good desoldering iron, you're probably going to have to spend a bit more. This is probably what your price range would get you:
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A little more at $265:
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A good tool is going to cost a bit. I admit that I really didn't want to spend that much on a desoldering iron at first, but it was well worth it. If there are any local pinball folks who do repairs, maybe ask if they can show you how to use it and give it a try.

I guess I understand the love for Hankos... they are promium consumer grade equipment as a somewhat reasonable price.
That said; I tend to be "eliteish" on my benchtop tools.
Metcal Soldering Irons
Pace MBT-100 Desoldering Station
and another high end brand for a heat pencil. Forget the brand right now.
All were had on Fleabay for an under 100-200 each.

I've been looking for a better de-soldering setup too. Right now I'm using a hakko soldering iron and a mechanical pump & braid wick when needed. That works pretty well with a chisel/shovel tip but sometimes there's just one little dot you can't quite get with intermittent bursts, but not often enough to rationalize the price of a quality de-soldering iron.

What I really want is to keep doing what I'm doing except replace the mechanical pump with a powered vacuum but if such a tool exists I can't find it.

I've been using this lately for everything and I have an electric de-soldering gun.
It's made by Vampire tools and costs a bit less than $30. High quality, the silicone tip is replaceable and doesn't melt with heat. The thing rarely clogs.
I call it the "high end cheap option".

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Just get the Hakko, it's well worth it.

Circuit Specialists has a six dollar 40 watt iron with a built in vacuum plunger. Looks really interesting. Some ebay sellers have them. https://www.circuitspecialists.com/soldering-irons

Had used old Radio Shack desoldering irons for thousands of desoldering operations (with the red rubber squeeze bulb). Thumb would get tired & no temperature control & tips wore out, but fairly cheap. Think you can still buy them. Yup, ECG brand $21 ebay.com link: itm
Or a no-name unit $20 ebay.com link: itm Use new tips for the fine work and save old tips for other jobs.

Me damage brain? Remember to wash your hands well after working with lead solder. Also drugstore 90% isopropyl is a cheap flux remover.

Been very happy with a rebranded AOYUE 8800 Desoldering gun sold by Circuit Specialists under their own brand. Looks like the older Hakko, but it may not be available anymore. Came in a hard side case with three tips, sponges, and cleaning tools for something under a hundred bucks on ebay.

I used the $10 solder sucker for years then upgraded to this ^ $30 solder sucker and thought it was great...then when actually doing serious board work....it sucked. not in the good way. I FINALLY sprung for the hakko desolder gun FR-301. WHAT THE F WAS I WAITING FOR. hands down the fastest easiest desoldering you'll ever do. Literally one use vs the solder suckers and you'll know you bought the right tool.

$19 at mouser, works well but i struggled recently with removing residual solder from through holes with it , will try wick or spring for a desolderer next time

I've been using the Aoyue 8800 and its served me pretty well. I think it was around your price point. I also just picked up a Hakko 703B. This station features 2 soldering irons and a desoldering iron. Not sure what I'm going to do with it yet, but if I keep it I'd probably swap out one of the irons for a set of hot tweezers. I'd be willing to sell you either one (prefer to sell the hakko honestly, just because I have a nice hakko soldering station already) for a reasonably good price sans whatever shipping would be.

I go full ghetto, and I likley do an above average amount of board work:

1. Cheap-assed pump
2. Scrap wire for braid
3. Solder paste

I've gotten really good at this mix and can desolder quickly and efficiently.

Make sure you clean the old solder out if you get this one, after every use. It clogs up relatively quickly. Works pretty good otherwise.

I wouldn't use it for your .156 connections on your boards you're trying to fix though, the vacuum solder pump you cock and push with a regular iron works a lot better for that. I know you've already added some solder to it that helps to desolder as well.

Yes, like the pic above. They work surprisingly well. Desoldering braid works very well, too.

I have a hakko and it's good of course. But honestly, a cheap solder sucker is quicker and works...even better.

Add some lead based solder w/rosin to the solder joint. Even a little flux on the braid helps. I've used some wicks that were just absolutely terrible, didn't wick at all. Most of the brands I buy are fine (I think they have flux in it).

I usually use the wick unless I'm removing IC's or connectors, then it's the desoldering gun.

LOL, I do the same thing. Buy the cheapest, then up it a bit, maybe another a bit better, then repeat as needed...then just buy what I should have bought to begin with in the first place. Ends up costing a lot in the end, at times.

I should add, my BlackJack desoldering gun I bought thru circuit specialists.com for ~$100 (now discontinued, replaced w/a newer model) really has worked great, no issues whatsoever and would buy again.

Hakko is the way.

You wont go back.

VEVOR S-993A Electric Desoldering Gun 100W temperature controlled. US $99.11. Ships from USA. https://www.aliexpress.com/item/1005003020680007.html

This might be the new budget option. Would want more sizes of tips right away, and wonder how good or bad the suction is compared to Hakko or the AOYUE 8800. Also available on ebay $113 ebay.com link: itm

Recall from a previous thread somebody took the ECG rubber bulb desoldering iron and replaced the bulb with a hose to a foot switch operated vacuum pump.

Look for a brand called Aouyie. It uses most Hakko parts but costs much less.

Myself and many other techs use this brand.

Its coming up for me on amazon too for $117. $10 off coupon on the page brings it down to $107. Another 5% back if you're using an amazon visa or credit line brings it down to $101.

Most likely the same seller shipping from the same warehouse but easier to get a resolution through amazon than aliexpress if there's a problem.

You made the right choice in this scenario. Second best choice would be to stick with the GTI lol. Man I miss my VW R32, especially seeing the money they bring in these days!

The pace I mentioned had two ports.
One for desoldering and the other for solder or other tips.

I have mine fitted with a thru hole desolderer. And alternate the other with soldering tip for rework wire bonding and a tweezer tip for removing smt parts

https://pinside.com/pinball/forum/topic/sucking-contest-vacuum