Picture is very red and slightly distorted

A fairly old model is listed here(KP-61v85) this answer is based on that model number:

If the set has not been serviced for a long time with set unplugged remove rear cover and locate (hard to miss) the three large black lens at top of chassis--clean the lens with a lens cloth or a paper towel with glass cleaner sprayed on the towel.

If the lens are dusty/dirty they will diminish the brightness and clarity of the the picture---they are the light source for the picture in this set.

Tv have a problems known as a convergence problems,it dead.The tv colors lines R,G,B mis alingments,have colors shadows pictures or 3D pictures look alike?The tv convergence board have dead 2 STK comvergence ICS and some or all it resistors are dead too.These parts on the tv convergence board,must be replaced to solved the tv pictures convergence problems.The shop,will cost like $300-350 for parts and labors.

The tv have a problems is known as a convergence problems,it dead.The R,G,B colors lines mis alignment,have colors shadows or 3D pictures.The tv convergence board the 2 STK convergence ICS and some or all it resitors are dead.These parts on the tv convergence board,must be replaced to solved tv picture convergence problems.The shop,will cost u $300-350 for parts and labors.

Double picture symptom shows tv got problem with convergence out section and most probably convergence out chips would be replace to fix this issue.
Though its job of qualified tv tech to replace convergence out chips yet I can provide you helpful info if you are handy with electronics stuff repair and can replace parts in circuit board as soldering work is needed with proper tools to repair tv.
Thanks.

the X or Y Sustain

On most of your rear projections you got GUNS and if there out of allignment or overheat you will get this error and it will need to be serviced.

Btw, I’m available to help over the phone in case u need at https://www.6ya.com/expert/edwy_1a56970cf1ea4620

4 blinks is error code in KP-61V85 and shows problem as follows...

IC1509(V out) is broken.
Q1505(V Pulse Buffer) is broken.

If you have no experience, don't put your hands in TV because TV has high voltage inside and electric shock risk involve.

convergence amp ic bad
Sony Convergence
http://www.techlore.com/blog/entry/19694/Sony-Convergence-Repair-My-Sony-TV-has-a-distorted-picture-/
http://www.techlore.com/article/19631/Sony-Convergence-Procedure/

Herringbone (and other patterns) can be caused my many faults, the obvious one the tech was looking for was a tuner/interference fault.

Another common cause is a faulty power supply.

Difficult to say without having the TV on the bench.

I'm a bit suspect about the $400 - $500 repair cost though.

Perhaps try another tech?

I doubt it's a DIY repair though.

Let's know how you get on.

Sony convergence problems
http://www.techlore.com/blog/entry/19694/Sony-Convergence-Repair-My-Sony-TV-has-a-distorted-picture-/

http://home.earthlink.net/~oleg.filippov/ConvergenceFix.htm
http://cmpalmer.blogspot.com/2006/11/fixing-my-own-tv-part-ii.html
Sony Convergence
http://www.techlore.com/blog/entry/19694/Sony-Convergence-Repair-My-Sony-TV-has-a-distorted-picture-/
http://www.techlore.com/article/19631/Sony-Convergence-Procedure/
look for the board that has heavy heat sinks on them the ic will be stk392-XXX
no experience in soldering i would send the board into ptscorp.com and have them repair it.