Indigest rhymes with:
digest, digest, congest, digest, gest, ingest, jest, suggest, abreast, acquiesced, addressed, addwest, arrest, assessed, attest, behest, bequest, best, beste, blessed, blest, breast, brest, bud-test, c'est, caressed, celeste, chest, chrest, coalesced, compressed, confessed, congest, crest, d'allest, depressed, dest, detest, digest, digressed, dispossessed, distressed, divest, dressed, eastern-west, este, expressed, farwest, fessed, fest, finessed, gest, guessed, guest, impressed, infest, ingest, invest, jest, key_west, lest, messed, mest, midwest, molest, natwest, nest, neste, northwest, norwest, obsessed, oppressed, penwest, pest, possessed, pressed, prest, professed, progressed, quest, rearrest, reassessed, recessed, reinvest, repossessed, repressed, request, rest, retest, self-professed, southwest, stateswest, stressed, suggest, suppressed, telequest, telewest, test, transgressed, trest, unaddressed, undressed, unimpressed, unrest, vest, west, wrest, yest, yoest, zest
Indigest sounds like:
inadequate, indexed, indicate, indicated, indict, indicted, induced, induct, inducted, inductee, intact, intoxicate, intoxicated