Here's the rule. Let's talk it out.
(b) Each candidate for nomination for President of the United States and Vice President of the United States shall demonstrate the support of a majority of the delegates from each of eight (8) or more states, severally, prior to the presentation of the name of that candidate for nomination. Notwithstanding any other provisions of these rules or any rule of the House of Representatives, to demonstrate the support required of this paragraph a certificate evidencing the affirmative written support of the required number of permanently seated delegates from each of the eight (8) or more states shall have been submitted to the secretary of the convention not later than one (1) hour prior to the placing of the names of candidates for nomination pursuant to this rule and the established order of business.[snip]
(e) If no candidate shall have received such majority, the chairman of the convention shall direct the roll of the states be called again and shall repeat the calling of the roll until a candidate shall have received a majority of the votes entitled to be cast in the convention.
It seems to me that names are placed into nomination only once, no later than 60 minutes before the first calling of the rolls. Additional calling of the rolls pertain only to the names placed into nomination 60 minutes before the first roll call.
Now, and here is the tricky part, it seems to me that delegates bound to a candidate for the first roll call cannot switch their statement of support before that roll call when the certificate of support is due; they are still pledged. Also, no new "white knight" candidate can be added after the first roll call, as calls for nominations and certificates of support are closed.
The only recourse is to fundamentally change rule 40 at the convention, which would require the cooperation of the Trump and Cruz delegates to reach an affirmative majority; or party convention managers can pull the voice vote "Ayes have it" trickery and trigger a riot.
-PJ
Here is the trickier part: there is nothing in the rules that says that a bound delegate must sign the statement of support for the candidate to whom they are bound. The only thing they are bound to do is to VOTE for that candidate for the number of ballots specified by their state. They are not required to support the candidate in any other way, whether that be voting for rules, delegate challenges or signing a statement of support for the nomination.