First off I'd really like a matchmaking system that tries to create balanced teams to ensure closer games (because rolling a bunch of noobs isn't fun, and getting rolled isn't fun).
Class saturation and diversity encouragement: Why not make it so that the class you pick has a shield meter determined by how many other people are playing that class? The more people using that class the smaller your shield bar, teams of just one class or mainly one class would be decimated while balanced teams would have little change.
Handicaps and limits: Top scoring players would have certain "perks" turned off based on how high their DPS currently is.... the higher it is the more perks removed. Perks like AT, UVs, and lastly armor damage perks.... for those not using any of these they'd see no change at all but those heavily reliant on them would be severely nerfed allowing the other team to push back.
Different map per game: Make it so that maps are randomized and cannot select a map from the two previous games.
Deathmark alert and Recon footsteps: For a "sneaky class" these two "features" severely punish those who play this class, just remove them of at least make them severely less noticeable.
HP pad scaling per tier: There is more than one reason that people don't play low tiers... one severely broken one is in T1 where guardians have the ability to sit on an HP pad and recover HP faster than it can be dealt to them, T2 isn't as bad but the pads heal the same number of Pips regardless of tier and control of the HP pad makes a game quickly decided.
Wasn't so heavy into the lockdown scene in the past. Since then one of the more intense players has become a good friend of mine, and opened my eyes to some insight into the game.
Here are the current problems with lockdown:
A) It is too easy to be a good striker, and too hard to be a good other thing.
B) Trinkets are still OP. You can be a good player with no additional weapon slots, but without trinket slots you simply can never compare to trinketed players - at least health trinkets.
C) Invinciframes do not accommodate your connection. The worse your connection, the less reaction time you will have. This makes better connections have superiority over all other players.
My solutions actually can be a bit more broad for these things. For B, make health trinkets scale with your total health. At +10, you'd have the standard +6 health. At +5 you'd have the health trinket -1. At base health you'd have health trinket -2. At +15 health, you'd get health trinket +1. At +20 health you'd get health trinket +2. This behavior starts at the 3* health trinket, and does not stack with other trinkets.
This makes it so that in lockdown as a striker you have a max of +8 health from health trinkets, a recon gets +10 from health trinkets. I would also boost the guardian health boost from +9 to +10, therefore it gets the maximum potential out of health trinkets (+6).
This also makes it so that health trinkets work more effectively in the clockworks. In the second half of tier 3, you'd get more health from these health trinkets, and in shadow lairs you get an additional boost.
However, keep the true love lockets at +6 health always. They are rare enough to be inaccessible to every lockdown player, but additionally ups their value and makes players actively seek them out. Pentas will be better later in the clockworks, but true love lockets will be consistent.
For C, have every 50 ping add an additional .25 seconds of invinciframes. If you have 100 ping you'll have half a second more of being invincible, at 200 you'll have a full second. This effect stacks up to 500 ping, at which case it stops any additional mercy frames. This means when you get disconnected you'll have 2.5 seconds more invinciframes, and if you play at 300 ping you'll get a second and a half more to react. This is helpful in both lockdown and PvE.
For A, really there needs to be more incentive to play as other classes. For example, a recon should be able to toggle their deathmark. When they cloak they should make a phantom set of footsteps in a 2 random directions, with their own footsteps disappearing after a moment as well. For guardian, their shield should only take damage once per attack (wide swing only hurts shield once even if it hits 3 people), and will not flinch when attacked. When their shield breaks, they should recharge their dash instantly the moment it breaks.
Other stuff you mentioned, such as map rotation, is a good thing. I hate getting frostbite 4 times in a row.