Shoulder season means late October to early March in Rome and Assisi, with Christmas excepted, and the months either side of summer in Lourdes and Fátima. Hotels are cheaper and the shrines run their full programs. The shrine of Fátima explicitly advises groups to avoid its May and October anniversary pilgrimages if they want time slots for private Masses. The existing guide on the best time to go has detail by destination.
Land-only booking lets a pilgrim use airline miles, fly from a cheaper airport, or arrive early on a low fare and meet the group at the first hotel. Sharing a room removes the single supplement, which is one of the largest avoidable charges; companies will often match solo pilgrims of the same sex who ask. Parish groups cost less than private groups because the parish fills the coach and payment plans are common. The existing page on payment plans covers that.
A day pilgrimage is a pilgrimage in the full sense of canon 1230. The United States has diocesan and national shrines in most regions, and the existing pages on U.S. and Florida pilgrimage sites list them. Admission is free at nearly all of them, and a parish can organize one with a school bus.
What not to cut: travel medical insurance. The State Department states that the U.S. government pays no medical costs for citizens abroad and that Medicare does not cover care outside the country, so an uninsured illness can cost more than the pilgrimage.