Re-greasing Sway Bar Bushings?

My 2016 Mazda6 has a Corksport Rear Sway Bar. After two years and ~10K miles, it squeaks when there's more than two in the car. Had two other six-footers in the car and the squeaking was comical for the first three minutes, then annoying as hell.

The bushings have Zerk fittings that are surprisingly easy to reach. What kind of grease do I use?

I bought this Synthetic MultiPupose Grease but there's no way to connect it to the Zerk fitting - unless there is some trick?

https://www.amazon.com/gp/product/B0081JE0OO

Here's the setup - it does have channels for the grease, which is encouraging.

While straightforward to get to, it's enough of a pain that I'd like to use the most long-lived grease so I don't have to repeat this often.

If there's no clever trick for adapting the squeeze tube to the Zerk, I can easily just get a grease gun cartridge of the right grease once I know what to get. Thanks!

I've used Never-Sieze with decent results.

I've used Molybdenum Disulphide with decent results.

I've used synthetic grease with decent results (Super Lube).

I largely ignore it; I don't like "maintenance."

Internet common knowledge seems to favor silicone grease with PTFE.  Super Lube puts a checkmark in both of those boxes.

Many (most?) standard grease guns will work without a cartridge tube.  For example the $12 HF mini-pistolgrip specifically says it can be bulk loaded.  So you do have the option of filling a normal grease gun using the squeeze tube o' grease.  You'll end up with air pockets in the grease, not ideal but also not a massive problem for greasing suspension bushings.

Amazon has at least one grease gun which threads on to a plastic squeeze tube and also attaches to a zerk fitting (others have only a needle or injector tip for bikes etc).  However, it is NOT cheap and no handle means no mechanical advantage for pumping.

I know that these bushings are designed to be greased, but the best method I've found for keeping poly sway bar bushings quiet is to wrap a few turns of Teflon pipe thread tape around the bar where it contacts the bushing. Keeps them quiet for many years and street miles in all weather.

In reply to obsolete :

This is truly GRM-level of super genius! Thank you. Yeah, this sounds worth the pain to unbolt the bushings because it's such a long-term solution.

Update: Disaster on multiple fronts.

1. The Grease Gun, cheapo from O'Reilly: https://www.oreillyauto.com/detail/c/performance-tool/paint---body/air-tools---accessories/grease-guns/fcdd362c0ffd/performance-tool-grease-gun/pfm0/w54204?q=grease+gun&pos=2

2. The grease from Amazon: https://www.amazon.com/dp/B00LXW06I0
It's white and thinnish. I was expecting the green super-sticky thick stuff FM used to sell with their swaybars (this is not an FM product).

Haven't used a grease gun since high school 30+ years ago, and not sure I ever loaded one. First major problem was the grease gun plunger seems to just scoot around the grease and not pressurize it. I ended up trimming the plastic cap as a piston, which helped. 60-90 messy minutes fighting.

Minor challenges reaching the Zerks, but it worked on the passenger side. I could see the new grease come out the sway bar bushings, so all good there.

Driver's side much tougher to reach - very hard to get the angle to put the grease fitting onto the Zerk and get it attached. Not sure I succeeded, but it felt like I got a few good shots of grease in, as well as several 'dry fires.'

The result is the major problem!! The sway bar squeaks ten times more than it did before!! Much worse. Very annoying.

I'm wondering:
1. Is this the correct grease? Too light and just ran out?
2. Did I get air into the driver's side and push out the existing grease?
3. Why isn't the plunger pushing on the grease and the gun working right?

I've got a friend with a lift and a grease gun filled with regular wheel bearing grease. I might try that and see if it is any easier. Or, take it to a shop and pay the nice people.

I don't think it's feasible to remove the bushings without hours of work I don't want to do.

Thoughts? Suggestions? Thanks...

First off, it could totally be the wrong type of grease if it's running out quick. You might want to try something thicker like that wheel bearing grease your buddy has. Second, air pockets can def be a pain, so double-checking your technique isn't a bad idea.

As for the grease gun issue, it's possible that the plunger isn't creating a proper seal, so that's why it's not pressurizing. Could be the cheapo quality showing its true colors.

Update for those glued to their screens at home: After another hour crawling under the car, it appears the culprit was loosened sway bar collars that were allowing the bar to move laterally. In some positions, the bar scraped on a curved/seamed bit of subframe, which was likely producing the squeak.

Centered and tightened everything and so far so good for five miles. It does look like the greasing worked, though if the original culprit was the loose collars, it may not have ben necessary. I'm wondering how well the collars will hold on slightly greased, painted/powdercoated sway bar?

Hopefully someone else can learn from reading this and avoid some trouble.