Checking Cauliflower

Understanding that fresh cauliflower is near impossible to clean (bugs.) Would roasting a head (or sections of) in a 600-700 degree bbq be considered a good cleaning method?

Thanks

Nope, does not help. It is not possible to clean cauliflower and therefore you should only purchase Bodek or similar where there are no bug issues.

Would freezing the cauliflower at home help? If it is truly “impossible to clean cauliflower”, how could there be Bodek ones available?

Bodek has devised a method under the supervision of a well known Rav who is expert in the field of insect infestations (Rav Shlomo Gissinger) to rid or not allow insects in its cauliflower and broccoli.
It’s precisely because of this, that we rely on them.
Your freezer suggestion while a valid attempt would Not rid the pesky insect from cauliflower, and with the many (up to 8) Torah prohibitions to eating an insect you should not take that chance.

My understanding was that freezing it breaks the bugs into pieces so there are no shlemim. Is this incorrect?

Incorrect.

Do you have any guidance as to any of the commercial hasgachot methods for checking vegetables - several offer a method for checking cauliflower - but that aside should they be relied upon? Asking specifically about eating at a restaurant.

Thanks

Checking cauliflower is basically impossible and should not be relied on. Only purchase cauliflower that was grown in a manner that does not present a bug issue altogether. Bodek, for example, has cauliflower that is ok to eat.