As a student who has recently picked up the HD 800 (used) and who has listened to a family-member's HE 560 extensively, I may be able to offer some modest help here.
First, the Valhalla 2 is regarded as a great entry-level pairing with the HD 800 from those whose ears I trust. Although I own a more expensive tube amp for my HD 650s that is more on the warm, lush side, I am looking into a Valhalla 2 myself since I think it will be more suitable for the HD 800s. You can always save for a totl amp later. I am also planning on doing some simple mods (Anax 2.0) that dampen the drivers and which helps ameliorate the tendency for the HD 800's cups to produce resonance, thereby taming the brightness that is not necessarily inherent to the drivers themselves. For the Valhalla 2, an OTL amp that eschews lushness and weight for neutrality and speed, this might be a good idea.
The T1s should also sound well on the Valhalla 2, but they are probably going to be no less bright than the HD 800s, and indeed may be even brighter. The caveat here is that I have never heard the T1s (I do have the DT 880 600s here though).
Second, the HE-560 is not going to work at all on the Valhalla 2. Your Magni 2U will make the better pairing here. The HE-560 is sort of like the HD 800s for planars, although some recent impressions are now claiming this status is even more true of the upcoming Mr. Speaker's Ether. HE-560 is highly resolving, fast on transients, has a large stage for a planar, and deploys a controlled and disciplined bass that hits deep only when the recording calls for it, featuring a tonality slightly on the brighter side of neutral. It images well but not as well as the HD 800, and its stage of course is not going to compete with the HD 800's. Yet its imaging and stage capabilities are exceptional for a planar, so you get all the benefits of the planar along with a relatively outstanding ability to analyze and separate sounds. I think the HE-560 would benefit eventually from a different amp, but since amps for planars are becoming increasingly cheaper, you are not going to have the same issue as you will with finding the "holy grail" for the HD 800. The Gustard H10 or Schiit Lyr come to mind as outsanding amps for the HE-560 at under 500 USD. FWIW I own the H10 and had the Lyr for a couple years (loved it).
Looking at your OP, I could not find what types of music you listen to. The HE-560 and the T1 (going from what I have read extensively) may be more versatile performers. I think the HE-560 is one of the best headphones for electronic music I have heard, but also renders acoustic instruments via folk, classical, and jazz incredibly vividly. You should really hear the violin on the HE-560 for a "jaw-dropping" experience.
It is a commonplace here that the HD 800 only excels with classical and jazz. While these "genres" sound very nice through the HD 800, I am also liking them with other types of music. It may be more accurate to say that most well-mastered recordings will be enjoyable out of the HD 800s, so long as you appreciate its capabilites. Since I have not heard the HD 800s through an amp more suitable for them yet, I cannot make any more meaningful comparisons here.
If you are a student wishing to save some money, I think you might want to make your first stop the HD-6XX pairing with the Valhalla 2. It is seriously an outstanding headphone that scales well with new gear, and it will also pair nicely with the Valhalla 2. You might really not need the feel to "upgrade" for awhile after listening to this pairing. The HD 650s are hitherto my favorite headphone!
TLDR: The Valhalla 2 is a great starter amp for the HD 800s but will not drive the HE-560s well. For this perhaps your Magni 2U would make a better start; other, affordable amps, will make the HE-560 really sing. I lack experience with the T1 but suspect it will be more generically versatile yet equally, if not more, bright than the un-modded HD 800s. HD 6XX should not be disregarded, especially with OTL amps such as the V2.
