Ok, some rough guessing here which may or may not be on target.
1ml = ~20 drops
Betadine = 10% povidone-iodine which is 1% active iodine
Lugol's is 5% iodine with KI
The Betadine at 2ml per 25ml is about 32ml per gallon. Times 1%/5% would mean that Betadine at that dosage gives about 6x the iodine as standard strength Lugol's dip.
Povidone probably does a better controlled release of the iodine than does the KI solution in Lugol's.
At your dosing rate, your dip is still 3x stronger than a "strong" Lugol's dip.
I'll give the Betadine a try. Probably less harsh on corals than Lugol's.
I've seen strong Lugols stun zoa nudis, monti nudis, and acro flatworms. I could believe that Betadine at 3x stronger would really do a job on those pests.