... How would Boat 1 prove that Boat 2 needed to tack also?
I believe your interpretations of rule 18 are correct, but it's usually a mistake to assume that a protest committee will share your understanding.
My advice would be (in descending preference order):
1) Don't get into this situation to begin with. Push your way up to the layline before becoming "about to round or pass" the mark. The rules are written to discourage tacking inside the two-boat-length-zone (TBLZ) and it's safest to avoid doing so.
2) If you wind up in this situation after all, hail the other boat before things get rushed. Tell them that you're inside boat and need room to tack. When both skippers know what the other intends to do, then they will most likely get through the encounter safely, cleanly, and without protest.
3) If the other boat won't give you room, don't break any rules yourself. You can head up, but you must try to avoid contact. Make sure you're squeaky-clean and then protest. If the other boat needed to tack to make the mark, then she will. In the protest hearing, be polite, present the facts clearly, precisely, and with good substantiating evidence. Testimony such as "I know were were overlapped for 10 seconds because I counted "one one-thousand, two one-thousand..." carries a lot more weight than "I guess it was 10 seconds or so". Tell exactly where the boats were at what times and it should be evident that tacking was required. Don't stop at the facts. Lead the protest committee through your interpretation of the rules, which ones apply, what each boat's obligations were, how you fulfilled yours, and how the other did not. Many protest hearings are miscarrages of justice simply and solely because people present their cases poorly.
Regards,
Eric