just dont buy little dot tube amp . I own little dot mk iv and love it and the tube sound. MK IV should be less warm and tuby then mk iii.
HD 650 were suffering with it, hights were suffering, felt recessed and even missing. Music lost its spark.
The sound was beutifull so warm and deep but at the same time felt somewhat sleepy and muddy.
Those headphones are allready warm so solid state should be the way to go.
Have you ever owned or listened to the E9 or the HD-650?
If you haven't, then you probably should not be making a recommendation.
As to the OP, avoid the cheap OTL tube amps. They cut way too many corners and most are disposable if something goes wrong. The only inexpensive tube amp worth buying is the Bottlehead Crack, and that's because you provide the labor. It is a nicely-documented amp and an easy build. $20 of tools will get it together.
If you're not willing to build your own and limit your budget to $300, you should go with solid state. Desktop solid state. You want power off the mains, not batteries, when running the HD-650.
I haven't heard the Shiit offerings, but people seem enthusiastic about them. One I can recommend is the Dynalo, at $300. Excellent circuit that has been kicked around here for probably close to 10 years. Older designs are still quite good - amp technology changes very slowly. The real benefit of age, however, is that it has been built by hundreds of DIY'ers and any flaws/shortcomings were spotted and stamped out years ago. DIY designs are open to everyone and reviewed by many people who understand them. Widely accepted DIY designs are often the best available at any price.
After some research around here you may find the Woo 3 has a nice following. A simple but well crafted and designed tube amp that is almost $500.00 usd new but can be had used from someone around Head-Fi for your $300.00 usd slot. The HD 650 is somehow a perfect match for this amp. The Woo 3 is not going to have the potatoes to drive something like the k701s well, but if there was ever a magic going on between two products it would have to be the HD 650s and the Woo!
Post an interest thread or comb the for-sale posts in Head-Fi and there is a good chance you may find one. Good luck.
A nice thing to note is unlike many manufactures you have Jack at Woo Audio as a great support source if you ever had questions or needed even the smallest service done on the amp. With this little extra it really makes the purchase of used a no brainer.