Google "Test tones" and you'll find a bunch of downloadable tones that you can use to sweep your system with.
I'm a retired EE and have a bunch of test equipment at my disposal so I've used a signal generator in the past to run frequency sweeps of my system.
The Home Theater groups have a ton of software that is for setting up systems that you might find useful too, but I just use sine wave sweeps.

Funny side not about the black grill cloth. My WAF went up considerably when I proposed doing the off-white/cream color vs doing black again. My preference is the black just because it strikes me as more "hi fi" looking, but I can't articulate a rational explanation for that. That said, as soon as I crossed over to cream, the wife was much more willing to have them in our house, especially since it came with a pair of DQ-1W subs!!

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Thanks Ed, but in this case I'm going to have to (respectfully) agree, disagree, and take a maybe position. I don't consider replacing the cloth a maintenance item. Most owners never do it and get by with original. It really doesn't degrade (maybe gets sun bleached if near a window but these weren't). So just as I wouldn't automatically repaint my car after 10 yrs., I don't think the cloth qualifies. And I also spent some time sanding and refinishing with walnut oil the rails so they look fresh and new again. The woofs - yes, If they go bad you're out of biz and it sounds it too. I wouldn't sell a pair that needed it unless I informed the buyer first and discounted to factor in cost to fix. Cap on the other hand sit in the middle. These 10's were working fine, with the original caps, so replacing them to me was more of a "preventative" measure dictated by their age. kind of like replacing your brake pads makes sense BEFORE you start hearing grinding from the rotor.

So based on this, I'd want to get back 100% of my cloth/cosmetic costs. eat the woofer costs, and price up or down based on the prevalence of 10's WITH upgraded caps vs how many are offered WITHOUT. Some buyers might, in fact, prefer to do their own upgrade of the x-overs and want them original, vs. already modified. For this reason, I'd consider auctioning them on eBay to get top dollar, but there's no way I'm gong through the hassle of trying to ship these things.

BTW - if anyone is looking for boxes, I recall I found some through Uline. Can't remember if they were already close in size or custom, but nonetheless, worth checking out if you're moving a pair.

Last but not least, there's the time factor in doing all three. For my part, and since there is no simple "how to" instruction guide out there for any of these modifications, there is a considerable learning curve if one wishes to do a good job and not much things up. I take the angle of really studying and then going slow so it looks perfect rather than cut corners and do a slipshod job I regret later. The grill cloth may look easy, but to get it right, it's a real bear and takes some real time. I've also seen refoam jobs that look terrible (excess glue all over, surrounds on backwards). So there is that to take into consideration.

The tinsels for the midrange dome are mounted on the driver's front plate and accessible without disassembling the driver. You can see them from the front of the speaker, actually, without any undoing anything other than the grill. The tabs you see are just mounted to pass throughs that the tinsels are then attached to on the front. The screws you removed should be replaced. Disassembly of the driver for access to the soft parts involves the four screws on the front, but you shouldn't have need to do that just yet. It's best to hold off on that as long as possible as it's difficult to center the voice coil of a dome driver during reassembly to prevent rubbing if you've not done it before.

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I don't have an example at hand (my parts and DQ-10s are in storage), but what sounds like might be happening is you may have bent the tabs when soldering to touch the topplate of the magnet structure. This would cause a short if both are in contact. This could cause crackling with intermittent contact. With firmer contact as you are applying during testing, while the crossover should still be presenting resistance to the amplifier in that case, it might reduce the system's impedance enough to be triggering the amplifier's protect circuitry causing it to cut out.

Of course, the crackle may be unrelated to the tabs shorting when you push them and may be due to a rubbing voice coil with the midrange dome. This will happen if the driver has been damaged from excess power causing the coil to unwind partially when the glue let go, but not enough to completely blow the driver. There is another case in that it might be the woofer that's blown. Dahlquist's documents indicate the tweeter and possibly also this driver would create a buzzing (high frequency noise) if the woofer was suffering a short. If you have an ohm meter handy, it'd be worth measuring both these drivers and seeing what you get.