I would be extremely worried about 2 different issues with making the pellets "mushy": #1 is that as soon as the pellets are wetted, they start growing harmful Bacteria and Fungi/Yeast, and the longer they are wet before they are eaten, the more harmful Bacteria and Yeast grows on them/in them. So by the time your bird is actually eating any of them, he's ingesting a very large amount of Bacteria and Yeast, both of which can and eventually will cause infections (2 different, separate infections at that) throughout his Gastrointestinal Tract, starting him his beak/mouth, then inside of his Crop, which is a perfect area for both Bacteria and Yeast to fester and grow, and of course this eventually causes the bird to not be able to eat anything at all because the Yeast will stop the Crop from doing it's job breaking the food down, and then it just sits inside the Crop and stops moving ("Crop Stasis"). And the infections will also spread through to the Stomach and specifically to throughout the Intestinal Tract, causing all kinds of issues...It wouldn't be so bad if your bird was eating the wetted pellets as soon as you give them to him, but if not, then it's a very risky thing to continue to do, especially if there is any mushy pellet remains anywhere inside of his cage that he might be prone to eating much later-on when he finds them...And then the #2 issue is that any mushy foods that you feed sexually-mature parrots of all species tend to cause hormonal-behaviors, just like putting any tents, "Happy Huts", boxes, etc. inside of their cages or touching/petting them anywhere but their head/face/neck does the same...It's too similar to what their parents feed them or to the hand-feeding formula their breeder fed them if they were hand-raised/hand-fed, as well as what they regurgitate and feed their mates before breeding with them...So a 5 year-old Goffin has may or may not have already gone through puberty (usually Goffins, if I remember correctly, first go through puberty/sexual-maturity and start producing sex-hormones between the ages of 4-5 years old, give or take)...I don't know if your Goffin has yet gone through puberty, but if they have not then you may notice that when they finally do hit puberty, they may become extremely aggressive with you, start regurgitating for you, try to mate with you, etc. during the times they are eating/playing with the mushy pellets (or any other mushy foods, such as oatmeal, grits, mashed potatoes, hand-feeding formula, eggs, etc.)...And this is a very serious risk with female birds, because anything that causes hormonal-behavior will also cause the production of Follicles and then infertile-Eggs that they have to lay, which is hard on their bodies anyway and often causes malnutrition, but most-seriously and dangerously presents the risk for Egg-Binding with every single egg they lay. So that's something that you definitely want to try to avoid at all costs....I believe Goffins are sexually-dimorphic, meaning you can visually tell their gender (I believe with the Goffins it's by the color of their Iris/eye), but only after they have already gone through puberty, because the visual differences between males and females do not present themselves until after puberty. So if your Goffin has the Iris of an adult male or female Goffin, then you'll know that he/she has already gone through puberty (I believe before puberty their irises are all-black, and then change after puberty)...Of course if your Goffin is already displaying hormonal-behaviors, then you already know that they've gone through puberty, lol...
On the flip-side, it is important that they eat a low-fat, high-protein daily diet so that they don't develop Liver or Kidney Disease (Fatty Liver Disease being extremely common in pet/captive parrots on all-seed diets)...I agree with Scott's suggestion of starting to introduce/try and see if he will eat all different types of fresh Veggies and dark, leafy Greens (Nothing from the Onion family, like any type of Onion, Leeks, Chives, etc., as they are toxic to birds, otherwise you can try any and all veggies and dark, leafy Greens as long as they are fresh and not canned (no watery Lettuce like Iceberg Lettuce or any Cabbages, as they contain no nutrition and just water)...This would help to supplement the necessary-nutrition that your Goffin needs to eat every day to stay healthy, and that he may not be getting because he's not actually eating much of the Harrison's pellets, but rather just playing with them...Just an FYI, fresh Fruit is NOT interchangeable with fresh Veggies and Dark, Leafy Greens, because all Fruit is full of tons of natural sugars, which are turned into fat and stored in the Liver; so feeding your pet/captive bird fresh Fruit every day is no better than feeding him an all-seed diet, the fat ends up in the same place and causes the same health issues. So fresh Fruit should only be an occasional treat, maybe 2-3 small pieces a week at most...And yes, wild parrots eat lots of fresh Fruit, they also eat lots of fatty Seeds and Nuts too, because they fly on-average 10+ miles every day foraging for enough food to meet their daily nutritional needs...Pet/Captive parrots walk 2-steps to the right and have a bowl of nutrient-dense food...So that's why you shouldn't feed them the same high-fat, high-protein diet that they eat in the wild...
I would check-out the Food/Diet forum here, because there are a ton of really great "Chop" recipes that incorporate fresh Veggies, Greens, grains, legumes, healthier seeds, fresh fruit, and fresh Herbs, and parrots tend to really enjoy and like different Chops, rather than just eating plain old Veggies and Greens sitting in their bowl...