I am neither a vet, nurtitionalist or breed expert ,however, as indicated above the food selector can be useful.
I note you mention three potential dietary health factors. You indicate a lot of digestive issues, you state your vet thinks there is grain intolerance & you think the dog has chicken allergy.
My personal unqualified opinion is that It would take significant skill, testing or specific ingredient elimination to properly identify any ingredient specific dietary intolerance or allergy.....especially in a puppy just 15 weeks old.
There are so many non dietary factors that can affect a dogs presenting as having "a lot of digestive issues."
Factors to consider might also include.......vaccinations, worming products, meds, flea treatments, illness, (including worms in wormed dogs), drinking old water (such as from puddles or outdoor sources), also floors are often licked by puppiies.
Scavenging can be a real issue. I say scavenging but I dont mean from human plates, this can be garden scavenging where the dog eats all sorts......from household waste spills, snails, fox or cat faeces etc, compost bins etc etc. Meal size, frequency, number of feeds, stress and exercise/play relative to feed times can sometimes be factors too. Puppies & young developing dogs can also be a little hit & miss as their young internals get used to solid dog foods.
I accept you may be an experienced dog owner so apologies if some or none of the above are worthy of your consideration (I have posted here not only for your potential benefit but also with future thread viewers in mind).
Assuming that food type is the sole or main issue you have to contend with then as you have been advised the food selector on here can be very useful. Ingredients & composition can be fine tuned in or out & budget can be factored too.
I wont recommend one particular food as your product requirements are likely to be factored by the above. I also note that your seem happy with current food albeit you seem keen to find a more cost effective longer term solution.
Personally I sometimes like to be fairly convinced as to the unsuitability of a specific ingredient before removing or blaming it. Not ideal to start removing important energy & key dietary sources from a young growing dog so I can understand why product trial and error is more often used......just be mindful as to the limitations of using this buy/try method if hoping to identify &/or eliminate genuine allergies &/or intolerances. In years past many dogs allegedly seemingly well fed on basic foods &/or human table scraps rather than hypoallergenic diets.
You have already recieved good food advice to effectively stay on what works (if food is acceptable) or to use the directory & option selector to see whether any ingredient/composition/cost acceptable other food options might be available without unacceptable compromise.
If you do decide to stay on or change foods & the dog settles on it (allow a few weeks) then perhaps share your choice , experience & reasoning for it.......this may also help somebody else (although every dog is different).
Good Luck & enjoy the still relatively new pup addition.