As is often the case, thinking through a problem from one perspective leads to a better mouse trap. However, thinking through the problem again, from an entirely different perspective, improves upon that mousetrap. Systems, conventions -- they all evolve and grow, if one constantly rethinks.
Consider the circumstance of a heart-based Michaels call. 1♠-2♠-P-? This is a much more cramped sequence, of course. Is there, then, a method for handling the "general invite" that is not so much fit-dependent? For, 3♥ might simply be a simple preference bid, which seems to force 2NT...3♥ as the invite, or does it?
What precisely is the meaning of 1♠-2♠-P-3♦? Long diamonds? If that is what Advancer has, could he not simply bid 2NT, expecting the likely 3♣ (happily surprised if not), and then convert 3♣ to 3♦? It seems, therefore, that the 3♦ call could be put to a better use. That use? A constructive heart raise, equivalent with the 1♥-2♥-P-3♠ sequence I described.
Of course, you may see the obvious now. If that option exists for a heart-based Michaels, then can we not restore the preemptive spade raise in spade-based Michaels sequences? Could not 1♥-2♥-P-3♠ be preemptive and 1♥-2♥-P-3♦ be a bid to show a constructive spade raise? That actually is my preference.
Back to hearts. The same basic structure over 3♦ as a constructive raise as was proposed for after a constructive 3♠ makes sense to me, tweaked somewhat:
3♥ = ugly, ugly, ugly -- very passable
4♥ = acceptance
3NT = diamond fit-dependent
3♠ = ???
Now, notice that 3♠ can show the club fit-dependent hand. We end up, then, with a bid of the "other major" for the club fit-dependent hands and the bid of 3NT for the diamond fit-dependent hands.
As to spade-based, after 3♦?
3♠ = ugly
4♠ = acceptance
3♥ = other major for club fit-dependent
3NT = diamond fit-dependent
Notice how each saves space needed for cuebidding.
Also notice that 4♣ and 4♦ are available for showing something different. The stand-out option seems to be that bidding the minor directly shows a need for a heart control, as this will be the most jamming bid and the least powerful position.
What do you end up with, then, as a scheme?
After a major-based Michaels sequence (1♥-2♥-P or 1♠-2♠-P), Advancer can bid 3♣ to play, 2NT...3♦ to play, or 2NT...P to play the minor. With simple preference for the major, Advancer bids the major at the lowest possible level, or can jump to 3♠ as "preemptive." With game or better interest, but fit-dependent, Advancer can ask for the minor and then place the contract.
However, if Advancer has constructive or better values, he always bids 3♦. Partner is expected either to sign off in the major (garbage almost beyond belief) or to bid the game (minimum range, but acceptance values). With the high-end Michaels hands, a concept that is not all that "high end" as we have seen, partner can make a slam move on route to game. His options:
1. 4♣ or 4♦ identifies the minor but denies a control in Opener's major.
2. 3NT flags diamonds and allows cuebidding space, and partner has shown a control in Opener's major. This allows 4♥ to be LTTC when Opener's major is hearts.
3. Three of the other major flags diamonds and allows cuebidding space, and partner has shown a control in Opener's major.
Now, a couple of other points might be noted.
First, a 3♥ call flagging clubs (1♥-2♥-P-3♦-P-3♥) allows two additional bids of interest, namely a three-level cue of the major (3♠ by Advancer) and a Serious 3NT call by either side. This wildly enhances spade-based sequences.
Second, a 3♠ call flagging clubs (1♠-2♠-P-3♦-P-3♠) does allow at least a Serious 3NT bid by Advancer. As these heart-oriented sequences are not blessed by as much space, and as no LTTC call will be available, the ability to bid or not bid a Serious 3NT here seems to be very important.
I'll leave it to others to work out the finer details of the follow-up sequences. However, one point that I would add here is that this scheme seems to have similar application to any related sequences. Thus, for example, if you play Cappelletti as your defense to a Weak 1NT Opening, then this scheme, incorporating a constructive+ 3♦ call, makes sense after a 2♥ or 2♠ overcall.
So, how about Michaels sequences for both majors?