There could be a number of temporal manipulation devices within the game, of which Astrobe's AutoPause might be considered one. An Instant Save device could be considered another.
F2-enter at a convenient Rock Hermit isn't quick enough? Though TBH, saving game in mid-battle is probably not going to end up with happiness and joy. I'm currently dieing - a lot - dealing with a Snakeman-Chryssalid terror mission in OpenXcom, and regretting the save point.
send that ship back in time, perhaps a week or so of game time, minus some or all of its cargo (perhaps any items bought within that period, if the game can determine these)
[...] If the saved gamedata is sufficient, the ship could, perhaps be sent to the location where it was at that time.
Hmmm, One of the trading OXP - I'm not sure which one - seems to keep track of your purchase prices ("32 TC of Furs @58.1Cr and 12TC @ 61.2Cr" - that sort of thing), but I don't think it keeps track of locations. So it's probably do-able, but at the cost of considerable programming and data storage for the OXP. A lot of work. A list of previous jump times and locations (vectors, "from" and "to") with the ship reappearing at the witchpoint in the appropriately-timed jump would be simpler than tracking the in-system movements.
a target ship's shield and energy levels are below certain thresholds will send that ship back in time, perhaps a week or so of game time,
The same time difference every time? So, you'll re-emerge into the middle of that firefight you had a week ago, just in time to watch the 17 ASPs blow your earlier self to smithereens then turn on your shield depleted ship.
I think it would significantly change game play, create all sorts of problems with self-referential paradoxes (for a start, were you to jump into a system/ time combination where your ship already existed, how is the system going to handle the clash of names? And what happens if you slip past that paradox, make a week's progress to your mission goal, get whacked again and time-port back into the system where there are two existing copies of your ship. One of which you accidentally kill. Like playing a "grandfather paradox" on yourself.
If you're looking for ways out of systems where you're getting a pasting, there are several existing OXPs that fit an additional fuel tank (1LY, or 3LY ; costing cargo space, or a pylon) which give you the option of getting out of Dodge under most circumstances. And when you're carrying a high-value passenger and jump into an Anarchy at 6.8LY range and no escape route ... you know what is going to be waiting for you. Good luck, Commander. Check your Escape Pod insurance.