I’ve done hundreds of these over the years. Every venue has it’s unique challenges.
I think a noise gate is not your best answer to the HVAC noise, rather, go with a Parametric Equalizer, which you can use in the field live, or apply in post. This enables you to isolate and minimize the specific frequency of the HVAC noise, wthout distorting much of the human vocal range.
Think about reversing the wireless lav thing: can you just have them wear yours, then run a second tap from your receiver to their PA system? Another approach that’s kind of unprofessional-looking, but often quite satisfactory, is to mic the speaker system, when you can’t get into the system cabinet for a hookup. Another thing: get your shotgun off the camera an onto a stand and get it up closer to the area where the presenters are. Finally, for audio stuff, you might want to check out Levelator; it’s free.
Using all shotguns in this kind of room may not be the best choice, unless each one has a human operator aiming it. IF the speaker stays in a defined area, an omni or cardioid dynamic mic or condenser mic might be a better choice, or use the lav mic under a lapel or pointed at the floor, it will still pick up voice well, but reject more room noise…. I’ve also had good luck using PZM boundary mics placed on a flat surface like a desk or lectern. The shotguns may be picking up more ambient reflection off walls than you wanted, compared to the pickup pattern of a dynamic cardioid…
Onto the camera issues: this is a classic case where you really want to have two cameras, one that is locked off to frame and properly expose the screen, the other, the presenter. It might be that your second camera is one placed remotely , if you can’t get your body and a tripod into the right spot. For some cases like this, I’ve brought along a consumer type DV camcorder which is very small and can be used with a tabletop tripod or a wall or door mount, for cut-aways and such, unattended. One neat trick for these is to make an adaptor for a mic stand that replaces the mic holder with a cheap dollar store tripod pan head and mounting bolt. Very unobtrusive and space-efficient means of backup camera placement, and you don’t need to carry a second tripod, just the screw-on head adapter.
In addition to the two cameras, or in cases where you can’t afford a second camera, you get a copy of the powerpoint slides and lay them in later, in post. You can play them full-screen, you can matte them over the top of the overexposed and illegible screen, you can create a 2-box picture-in-picture effect of the slide and the presenter. I always favor shooting mostly the person in these things, rather than the slides, because face it: the person is the component that can’t be re-aquired later, the slides pretty much always can be gotten again later. Sometimes, I would get to the venue early, or stay late, and set the camera up right up close to the screen, and I’d just shoot ten seconds of each slide in perfect focus and exposure. Then I wouldn’t have to worry about choosing between them and the speaker, later, during the actual presentation. The trickiest bit is when speakers stand right in front of their projections and do shadow puppetry or whatever, or play with laser pointers. Not that much you can do about it, except fix it in post.
You can even out the lighting, if the projection is strong, by hitting the speaker position with an independent, diffused, spot light, to get him a little brighter, and thus reduce the brightness ratio between projection and speaker. Or, you get in there ahead of time and tweak the projection settings and positioning. This will help you with iris management. So will the application of shades or barn doors to the projection system, where possible.