Character Concepts you wished would work in D&D?

[Morphic tide]

With regards to Vestiges being problematic for 5e, think of it as occupying the possibility space of full-list preperation like Clerics and Druids, and work around that. Most of the same concerns apply, and it respects allowances for re-binding and multiple simultaneous Vestiges. Acts quite similarly to the Mystic's Disciplines, where one selection gives a variety of abilities, but related in a looser fashion. Mixing the two gets weird, but the degree of mechanical variety spells carry is greater than what Vestiges have done historically. It need not be subclass level distinctions implemented. The "big sell" being a floating Proficiency or two is certainly interesting, but not necessarily overpowered, especially given how much of that there are already spells to bypass.

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With regards to a shapeshifter class, the underlying problems are rather direct mechanical issues with how shapeshifting is handled in 5e. My own suggestion is in limiting how much can be added to your base statblock instead of having the functionality be replacement, with some form of "slots" for pushing beyond your default and the "free" allowances regarding natural attacks, movement modes, AC and such, heavily keying off Monk for these at-will benefits. Archetypes then focus on increased applications of those slots and better imitating particular enemy behaviors, such as one dedicated to emulating Legendary actions and resistances as the "area damage" and line-holding option, while another may focus on being a chimera that can swap out pieces and outright make things up rather than being left to the combinations of effects the world around you has to offer.

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Expanding on Disciplines is easy. They're derived from the 3.5 Ardent's Mantles, and are a list-based feature, so they're quite expandable. The key thing to do is to split the subsystem, dividing Disciplines according to party roles, and focus on different takes on the role. For an example of distinction, the class I'd base the canned gish upon would be the Lurk in its capacity as skillmonkey-with-subsystem, while the Mystic would turn into a support manifester, offering great plot powers and considerable buffs, but simply lacking save-or-suck, blasting and personal transformation. All varieties of in-your-face murder then go to the Wilder, whether it be becoming a bigger, meaner murderbeast or launching stupid amounts of direct damage, alongside overlapping combat shutdown Disciplines with the Lurk.

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Adding a new Martial is something I'd love to do. I'd go with doing stuff on Hit Dice, as it's a resource almost untouched in the rules and we lack a healer rooted in low-level mechanics like the Fighter and Barbarian are. More of a forceful taskmaster vibe than previous versions of the concept, such as a lot of 4e Leaders. Baseline, the healing would only be the standard Hit Dice dragged into combat, as well as being able to have them be spent for various purposes. Possibly lean on the Bounded Accuracy rules with the "Warlord" adding their Charisma to cover for rolling a hit die instead of a d20 for some kinds of task. Immediate archetypes being a "sawbone" to make Short Rest recover of hit dice themselves open up, as well as a self-harming berserker flavor.

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The task of making a balanced summoning-focused class has two forks: Mass summons, and having one big summon. The former needs mass combat rules to "batch" attacks into gradual defenses to cut down on rolls and handle blocks of creatures moving at the same time. The latter is vastly easier, as it is a matter of having the primary character be an external battery for a semi-disposable creature. Said large creature ought to be a bit of a glass cannon, as it receives considerable healing from the primary character and its death is not likely to be campaign-ending. Doing both in one class has other issues, mostly regarding how you end up with such a large number of health totals to track (though again, rules to batch things into gradual defenses can help a lot).