Jonathan,
So, it sounds like you have multiple issues going on here. Vouchers were paid that should not have been. Physical checks were printed on but with the wrong check number. The wrong bank account was specified.
Given that the keep check process used the delete all option, the payment selection batch is just sitting out there ready for another check run. However, it includes vouchers that should not be paid and has the wrong bank account associated with it. As you stated, it makes sense to just delete that payment selection batch and start over. You can do that by going back to the payment selection screen, use F3 to select that batch and then use the delete button on the toolbar to delete it. The only issue with this approach is that you have a set of physical checks that have been printed on that will be destroyed and this approach does not allow you to mark those as void within SL. Not marking them void causes no integrity issues within SL but will leave those check numbers unaccounted for within SL. If it is important to account for those destroyed checks within SL then you could run the check print step again using this payment selection batch printing to plain paper but specifying the starting physical check number actually used and then, on the keep checks screen, use the void all option. That will mark those check numbers as voided, complete the payment selection batch process but leave the vouchers that were included as open items for another payment selection batch. If some of the checks in this first run are actually good, you could do as above but use the select by check option on the keep checks screen keeping the good checks and voiding the bad checks.