I think your take on the issues with the Circle of the Moon Druid is a fairly reasonable one. Having played a one through to level 14, I agree there is a strong incentive to ensure your Wild Shape is available for combat as it is one of the strongest combat features in the game.
I'm going to address your features seperatelyseparately as I don't believe there is a strong reason for them to be tied together and players/GMs could easily use one or the other without consequences.
Given that you are grantedgranting a feature and taking nothing away this is inherently a power positive change, however I don't believe it is a bad one. A lot of the utility power of Wild Shape comes from being able to choose the best possible form for any given situation at a moments notice. By restricting to one (later two) forms you remove that ability and make this a fairly minor feature overall.
The benefit to roleplay and the "feel" of playing a Druid is far from minor. I, and every Druid player I've played with, would have loved this feature from a purely roleplay perspective. I believe you could even grant it earlier or raise the CR limit to 1 (but not both) without introducing a game breaking change. This feature doesn't really enable the Druid to do anything they couldn't do anyway but removes the need for taking a short rest immediately after, slowing down the game.
The healing from your feature is so minor as to be basically meaningless at this level of play. Expected damage would be in the range 50-100 points per round rather than per minute so the healing won't make a meaning differentmeaningful difference to combat. It is also unnecessary between combats as you regain wild shape at the start of each combat and can always shift into a new form instantly regaining maximum hp.
I suggest scrapping the healing feature and instead granting 1 or 2 additional uses of Wild Shape at this level. That should better mimic the feel and power of the original feature while removing the more broken aspects.