What you are doing with relativity is not aging one item, while aging another item.
Is it better to just put your treasure in the deep freeze?
Typically much of what you do with space is "coasting". The expensive part is the initial acceleration. So, once you get up to speed, you could technically maintain that speed/time differential forever.
However, you will have troubles reversing your object as you may need either a black hole, or to pass by a series of stars. And there are not any black holes that we know of anywhere close to Earth. Hmm, can you even do a "slingshot maneuver" at the speed of light, as the method for doing a slingshot is to accelerate towards the object, and reach the highest speed at the closest point near the object, then decelerate as one departs. The problem is that if you are already at lightspeed, you aren't supposed to be able to accelerate to a faster speed, then you loose some speed as you depart from the gravity pull of the object. Anyway, I believe you need the black hole to get adequate inward gravity pull (centripetal force) to reverse the direction of your near lightspeed object. And, if done right, it will be a weightless maneuver, so you won't squash your astronauts. Just make sure you stay on the right side of the event horizon.
Earlier, I tried to do the calculations of how much energy it took to reach the speed of light by looking at momentum and kinetic energy (with classical mechanics).
p=mv (momentum (kg*m/s) = mass x velocity).
And Kinetic Energy:
= (1/2) mv2
Substitute in c for v, and one gets:
= (1/2) mc2
With relativity, you add the Lorenz factor
p = γmo
And, as you approach the speed of light, you multiply in a factor approaching infinity, and both your momentum and energy go towards infinity.
But, even with classical mechanics, one finds:
= (1/2) mc2
With the famous: E=mc2
One finds that to accelerate 1kg of matter to near the speed of light (classically), it takes the equivalent amount of energy as converting (1/2) kg of matter into pure energy.
Now, a couple of other equations.
Say you want to keep your acceleration under 10G's, or say 100m/s2
To reach the speed of light, it would take:
= 2,997,924 seconds / (60*60*24) = 35 days of just over 10G acceleration.
Say you made a track in a loop around the moon, you'd quickly go beyond your specified 10G's centrifugal acceleration long before you get to the speed of light. Likewise, if you could install a track around Jupiter (which would be hard due to it being a gas giant), you would still quickly get to your 10G's centrifugal acceleration.
So, you really have to use an onboard energy source. I.E. a lot of antimatter, and consuming most of your ship.
Also, I really wouldn't recommend aerobraking for the same reason it takes about 35 days to get to the speed of light, and the heat and friction coefficients (would you really want to dump the equivalent of half your mass in pure energy in a matter of seconds?) .