Seems like a lot of work...unless you are just hell bent on retaining the OEM arms...if that's what they are.

Street Performance Lower Control Arms 64-66 Mustang – Falcon Comet – Opentracker Racing

opentrackerracing.com

What I would do...

Roller Lower Control Arms – Street Performance / Drag Racing – Early Falcon & Comet (1965-1966) Mustang – Opentracker Racing

opentrackerracing.com

Then it's just a nut and bolt job...and likely an alignment.

 

What condition is the ball joint? Is it also 60 years old? If so, I would just replace the LCA with a new one. If the ball joint is fairly new, and the boot doesn’t tear when you remove the LCA to replace the bushing, a hydraulic press or ball joint press would be needed to do the work. Examples:

https://www.harborfreight.com/12-ton-h-frame-floor-shop-press-70604.html

https://www.harborfreight.com/ball-joint-service-kit-for-2wd-and-4wd-vehicles-63610.html

 

I recently replaced both lower control arms on my 67 coupe. It was not as difficult as I thought it would be. The difficult part was separating the lower ball joint from the spindle. The lower control arms were originals, so the lower ball joints did not want to part ways with the spindle. Its best/easier to just replace the entire lower control arm. I bought the Open Tracker Street Performance lower control arms:

Andy Kruse has a great video on how to replace the lower control arms:

How to replace the Lower Control Arm - Classic Mustang (youtube.com)

 

I have a 69 but echo the "replace the whole arm" message. I got mine from Open Tracker

 

To answer the original question, to replace the bushing, heat the bushing tube with a propane torch until the rubber starts to smoke. This breaks the bond that's formed between the rubber and the bushing tube. Then immediately smack the end of the bushing with a hammer, holding it over a bucket of water, and the bushing will pop right out. It's really quite simple.

I normally use a press to install new bushings, but you could also use a vice, clamp, etc.

 

New lower control arm: $25
New lower control arm ball joint: $25
Lower bushing: $10

For the $$, replace the whole arm.

 

Thanks everyone. Looks like I need to rethink this one!

I CAN confirm, however, that replacing 60 year old sway bar end joints and strut rod bushings dramatically improves handling.

 

65-66 Lower Control Arm MOOG Made in USA

 

I've never replaced that kind of bushing on any of the steering parts or leaf springs over the years, always just replacing the assembly. However, I get why an owner may want to try. It would not be a time or money decision, more of an "atta boy" feeling of fixing the existing original part myself! Reading Lizers post it seems like this bushing would be fairly easy to do......I bought the Opentracker roller lower control arm rebuild kit and finally finished the arms after 2 or 3 years of on and off fooling with the modifications to a pair of original 65 units. This was not a job for the faint of heart with limited skills, but I learned and enjoyed the task rather than view it as a hassle. Of course, this led to me ordering more stuff from John like cheater upper control arms, adjustable strut rods, a roller drag link, and Bilstein shocks to install everything over the next week or so. The struggle is real! Have fun with whatever you decide!