True polymorph says:

Creature into Creature. If you turn a creature into another kind of creature, the new form can be any kind you choose whose challenge rating is equal to or less than the target’s (or its level, if the target doesn’t have a challenge rating). The target’s game statistics, including mental ability scores, are replaced by the statistics of the new form. It retains its alignment and personality.

I assume it changes the creature's type as well.

Magic jar says:

Your body falls into a catatonic state as your soul leaves it and enters the container you used for the spell's material component. While your soul inhabits the container, you are aware of your surroundings as if you were in the container's space. You can't move or use reactions. The only action you can take is to project your soul up to 100 feet out of the container, either returning to your living body (and ending the spell) or attempting to possess a humanoid's body.

Question:

Is it possible to true polymorph a non-humanoid creature, wait for an hour to make changes permanent (so one doesn't break concentration), use magic jar, possess target's body and then dispel true polymorph with dispel magic thus gaining all the perks of original host's body?

This would not work.

Unfortunately, although everything leading up to it works, including dispelling true polymorph, once your have dispelled the polymorphed creature back into it's original form, it is no longer a valid target for magic jar, and thus the spell would end.

This sage advice tweet from Jeremy Crawford suggests as much:

In #DnD, the exceptional trumps the general. (No longer being a valid target trumps condition carryover.)

The same reasoning is used for this answer to a similar question about targets of spells changing from valid to invalid after being cast.

This works

While we've had Jeremy Crawford, lead designer, rule on dominate beast, that case is different as the effect is also tethered to the creature type (emphasis mine)

While the beast is charmed, you have a telepathic link with it as long as the two of you are on the same plane of existence...

In the case of magic jar, the initial possession requires a humanoid target, but the following effect only specifies creature (emphasis mine):

Once you possess a creature's body, you control it. Your game statistics are replaced by the statistics of the creature...

Meanwhile, the possessed creature's soul...

This is also somewhat reinforced by Jeremy Crawford's ruling on Charm Person:

There's no rule governing what happens when a valid spell target temporarily becomes an invalid target. A good rule of thumb is that the spell is suppressed while the target is invalid

Clearly we have no specific rules clarification and need to determine whether a target is valid to use Crawford's rule of thumb here. The target for the activation of magic jar's possession is a humanoid but once the target is possessed the language used is "creature." As long as the target is a creature, the remainder of the effects are sustained as humanoid is no longer a requirement for target validity.

Credit to Tim Grant originally for his answer on a similar question.

Ask your DM

There is enough ambiguity in the rules and in the tweets by Crawford cited in the answers by David Coffron and NathanS that this will mostly be left up to the DM to determine if it's reasonable.

Yes, but remember Magic Jar can be dispelled too.

Magic Jar says it ends when dispelled:

Duration: until dispelled

Dispel magic only automatically dispels level 3 or lower spells, but there's a chance you dispel higher level magics (or use higher spell slots, but I digress).

True polymorph - level 9 spell

Magic Jar - level 6 spell

So, you could try it, and hope you only dispel the polymorph and not the magic jar, but polymorph will be more difficult to dispel (Your DM might be nice and allow you to try to target just the polymorph spell).

Even if you get yourself into this somewhat precarious situation, a dispel effect would unravel the magic jar.

Magic Jar would give you a pretty sad ending:

If the container is destroyed or the spell ends, your soul immediately
returns to your body. If your body is more than 100 feet away from you
or if your body is dead when you attempt to return to it, you die. If
another creature's soul is in the container when it is destroyed, the
creature's soul returns to its body if the body is alive and within
100 feet. Otherwise, that creature dies.

When the spell ends, the container is destroyed.