what size motor 350? sounds like a low torqe stater you may have a high compression motor or just not enough cranking amps ,you might need a bigger battry ,big block motors do the same thing ,a high torqe starter cost more but will solve problem if you have high compression , i had the same problem with a 455, my starter was standard so i replaced it with a high torqe and fixed it....
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Sincerely,
Michelle B.