How should I encourage a firm to speed up interviewing process given progress with another

I'd like some help for a present situation. I'm currently interviewing with 5 firms, 2 of which are "A+" (referred to as A1 and A2) and 3 are solid "A/A-" firms.

I've been through 3 rounds with A1 and just received info to prepare a case study. I'll be presenting my info next week. Assuming it goes well in the presentation, I expect the firm to be extending me an offer with likely a few days to consider.

I got connected to A2 through a mutual connection and really hit it off with the guy I interviewed with. I've completed a first round (with mutual connection) and trying to connect with the MD of the group for the second round. The MD is in the midst of a lot of stuff and I haven't been able to get time on his calendar yet.

From a timing perspective, I'd like to have offers from both firms at the same time to be able to better negotiate. I want to send a message to the A2 guy I interviewed with letting him know I'm approaching a final round with another firm. My concern is two-fold: (1) I tell him about the progress as A1 and worst-case scenario, I don't get an offer at A1 and he asks, I'll look like damaged goods, (2) I don't tell him that I'm at that stage and I have to make a decision on A1 without knowing if A2 wants to move forward.

Curious if anyone has guidance on how best to communicate with the guy at A2? Planning on sending him an email today but want to make sure not to be too pushy but also don't want to make my mutual connection look bad if I take another offer and leave A2 in the dark about my other options.