Ralph,
Welcome to the Forum! The outhaul can and should be replaced. The original design is only a 2:1 purchase inside the boom, the blocks inside are of questionable quality, and the small plastic covered wire is not up to the task. About 4-5 years ago I wrote an article for Mainsheet on just this topic, complete with photos and a parts list. I know that it's on the Tech Notes CD. All three year memberships and renewals in C36IA receive a free copy of the Tech Notes CD. They are probably stuck on with corrosion, but the end caps have to come off. If you were able to get the four self-tapping screws out, you've got most of the job done. Others have had to drill them out! It might be best to take the boom off the boat and work on in your garage or workshop. You might need to soak the ends with PB Blaster and/or use heat. The bolt thru the end cap does not have to be touched. Hope this helps.

Trying to find a link or a pdf version of this mainsheet article Tom wrote. Any idea how to find it?

It would be great actually to motivate people to subscribe as full member to have links to the member section referenced in the public section. Like for this article, I am already a paying member, but if I see I can get more, I am sure I will be even ready to pay twice :)

The writup (with pictures) is in the Feb 2005 issue of Mainsheet.

Screws "removed"! Now I guess the next step is to heat it and use a hammer to get the boom end out.

Lots of kroil and gentle  tapping with a punch will get them off.   Doubt mine have been off since 1983 when I pulled them this winter to replace the outhaul.  

OK making progress but now not sure yet how to get the outhaul out, is there a wire to rope splicing?

Do you think I need to remove the boom and open the goose neck side?

Goose neck end just remove same four screws as on the other end and remove that end cap

I replaced on my C30. Yes, use a penetrant like PB blaster. I used a wide screw driver blade and tapped it with a hammer- alternating sides and eventually removed the endcap. On the C30, and maybe on the C36- I found lots of mounting screws from external blocks and slides extending deep into the boom interior- often hanging up the out-haul line/block. I had to remove them and shorten to correct the problem.

Completed the upgrade 2 weeks ago and tested on a 70 nm trip this week-end. It works great!

Replaced both sheeves with sheeves bought on Catalina Direct:

Mast sheave:

• H1883 Masthead Sheave Ball Bearing C-25, C-27, C-28; Outhaul C-28, C-30, C-34, C-36 ($39.95)
• I think it's overkill and a bit too much money for the job

Aft sheave:

• Masthead Sheave Wire C-25, C-27; Outhaul C-28 to C-36 ($8.95)

Built the new purchase with:

• Harken #085 Double Block w/Becket (ebay $25.39)
• Harken #086 Triple Block (ebay $29.99)
• 30' x 1/4" Sta-Set New England (west marine $19)

Replaced the self tapping screws with 8 x ¼-20x3/4” SS machine screws, shorter would have been better, but it was I had in my boltdepot kit when I did the work.
 

Put a lot of Tef-Gel to hopefully have an easier time next time I want to look at it.

Thank you to Tom, Les, and all the materials available here! It helped me a lot to go over this project.