What is the average number of quality analyst interactions per month with a pool of 4-6 key spokespeople to provide briefings?

It is dependent on a few things. Are all of these people talking about the same product, different markets? What is the pace of development? Are these people subscribers? What level are they? If you do not subscribe to a firm, you're limited to briefings. An analyst will take a briefing 1x per year from a non-client. You do not have the ability to do inquiries at all. If there is an update or such, then you can probably get an additional briefing. If you attend events where analysts are, you can pitch briefings and add extra touchpoints. If you are a client, you could probably brief 1x per quarter. It isn't about the subject matter experts necessarily. It is about the analysts' time and how much they need/want to speak to that SME. It is also dependent on your entitlements as a paid client. If these SME's have a Gartner subscription, they should be speaking 1x per month to key analysts through a combination of inquiries (paid entitlement) and briefings (when updates or key news come up). Other analyst firms are more liberal with their entitlements (subscribers vs. non-subscribers) for inquiries and you may be able to get groups together to have a good discussion. SAS days where you can consult with an analyst with a group of SMEs have largely disappeared but they used to be very valuable (but expensive). I do one SAS day per year or so now with a non-Gartner firm.

Employees designated as spokespeople should be in touch with their market on an on-going basis with about 2 two specific touchpoints per month if not more frequent - this could include PR interviews, podcast, analyst inquiries and briefings, customer/prospect interactions, speaking opportunity.
Getting on a cadence is beneficial to ensure sustained engagement with the market.