…staying up Shovu’os nite, and praying @Daybreak come Shovu’os morning, there is a tremendous unresolved sofek laHalocho if you can make a Benediction on your Tallis Kotton, which has been on you all Shovu’os nite. … By wearing a Talis Godol, you evade & avoid this entire issue, and can peacefully bless over it, without any compunctions whatsoever…
He could also take it off before morning or put on a different pair.