A "pushed out willy" is, in veterinary speak, a "prolapsed penis".
The primary cause of this condition is not sticky poos/difficulty in pooing - for anybody with an iota of boar experience, they will firstly look to the possibility that it is fur/hay/gunk that has found it's way into the foreskin and wrapped itself round the shaft of the penis (often happens in older boars, especially those with longer hair)
I therefore think you have two issues -
1) his prolapsed penis and
2) his sticky poos
They need to be dealt with separately unless and until it can be categorically shown the two are interlinked....(and your current vet has "speculated" rather than "proved" their diagnosis)
So let's deal with the protrurding willy first....you will probably need tissues soaked in cooled (but still warm) boiled water, some cotton buds, some KYjelly. Sit on the sofa with your piggie upright but his back nestling either between your legs or on your stomach (on a towel!) . This will help support him comfortably and thus give you both hands free to gently extrude his penis to its fullest extent. You may find lots of greasy yellow/cream/white covering - wipe this off gently with tissues or cotton bud soaked in warm water.....you may find fur/hay wrapped around the upper shaft - gently remove/un-entangle this with your fingers and tease the rest away with a cotton bud. Most importantly - don;t "yank" it. If necessary you may have to put his bottom in a wash basin/bowl of warm water to loosen it all first.
Once you are sure you have removed all the gunk" from his extruded penis, apply KY jelly and let it slip- back smoothly into the sheath.
Repeat as often as necessary ( I have a 7yr old boar with a penis that routinely sticks out because he gets fur and gunk around the shaft - I clean him once or twice a month as above which normally involves a pre-soak in the wash basin first! - )
Secondly - the soft gunky poos - this is more worrying as there could be a number of causes but most often it signifies a dietary deficiency/imbalance caused by either pain or infection.
Firstly take him off all veg - and give hay, hay and more hay. Provide also some ripped up kitchen roll or newspaper and see if he eats it as this will indicate whether he has a digestive disturbance and needs more fibre.
Weigh him daily and monitor his food intake and his poo output. If he is losing weight you may need to supplement by syringe feeding Supreme Recovery or Critical Care (or his favourit pellets softened in warm boiled water and then homogenized) Also put a bowl of water in the cage as he may not wish to bite on the bottle tube.
The soft poos suggest his gut is not functioning properly so a course of zantac (2mg/kg) may help stabiliise the gut. It will NOT however cure the cause - it will merely help alleviate the symptoms
Having stabilised his "symptoms" as above, you then need to find out hat has caused this. I note you are in Glasgow - and unfortunately we are STILL not aware of any decent cavy savvy vet in Glasgow - your best cavy savvy vet is Glen at Apex vets in Denny/Falkirk.
You may need to have a poo culture done to check there is no infection/.parasitic burden. It may be he has developing dental problems that have caused the poo issue...it may be he has another underlying issue (such as stones.infection etc) that has caused him to develop gunky poos.
Sorry - this is a lot of info to take on board in a short space of time....if you have any questions or want a chat on the phone then please PM me.
x