Comments on DM or SPAM ASAP (actually even affiliate DMs) approaches
It pollutes you and your follower's messages/profiles/feeds/notifications, especially if you run it using your main account.
It typically goes against most platform's ToS and best practices.
You don't have to move all your followers at once. It's likely that you will still be using this platform, but would like to recommend your other content to them.
You can alleviate this by sorting by value, perhaps by number of followers, some kind of engagement metric.
Revising assumptions
Your followers are other agents who find (or once found) your content engaging.
Engagement between agents wax and wane, since content, preferences, interests, discoverability change over time.
Good engagement is temporal - it's fresh in your follower's mind, perhaps because you posted a series of very interesting content then they favorited, retweeted, and responded to.
Good engagement is mutual - when you respond to each other, there is a relationship formed.
Good engagement is historical - you can "index" engagement using weights for favoriting, retweeting, responses, mutual engagement, recency, etc.
A notification/recommendation from someone else to approach content from another author is not necessarily of less value than when given by the author themself. In some cases it might be even better (for e.g. a recommendation from author vs from Goodreads or a friend).
You have resource limits (API calls, time, money, patience/goodwill from followers)
Pros
Recent tweets are easily available, and might be more representative of recent engagement levels
Doesn't pollute personal space, works just like a recommendation bot
Can "clean up" tweet space after time period
Followers have the option to receive an opt in prompt, or mute this 3rd party profile if they never want recommendations
Can use DMs, mention tweets, maybe even reply and highlight recent engagements as a prompt for other content
other users that see this recommendation based on a "hot"/valuable discussion has more immediate impetus to check out the recommended content as well
Cons
Service reputation starts from scratch <<< high profile reputation
Shared API resources
Needs to keep track and index engagement - seems like an exponential problem when considering number of agents in system
Might be alleviated if we can use Twitter's notification API for likes, replies, retweets, though limited to Premium/Enterprise only
I'm thinking of a different approach:
Comments on DM or SPAM ASAP (actually even affiliate DMs) approaches
Revising assumptions
Pros
Cons