2A ?!?! Got lost there...Where does those 2 A come from ?!?
USB, for example , depending on the version deliver between 500mA and 900mA.
So where you got the 2A from ?! Or have i missed something ?

Dont get me wrong, but seems you have a string of deception going on already, on this forum...Is this another one ?!?
But maybe your details, as asked, might sort you the required things. 

And i bet Grumpy_Mike will agree with me when i advise you to learn the basics of reading datasheets...might seem scary, but it aint. Start with the things you really need, and slowly grow from there !!
Plus will save u lots of hassle and hours, not only in the short but specially in the long term.

difference between them is that the 7000 series is designed for high frequency operation and the 4000 for more analogue ones.
Example- the two you mentioned: the 7xxx goes up to 55mhz while the 4021 up to 12mhz.
Apart from that, they pretty much do the same

the tutorial explains it quite well. Also advises the 10e10ohms wirewound resistor on the 5 V( as its the one who carries more amperage) in order to reduce it enough for breadboarding projects. So its all there on the link u placed here

Yeah, i totally agree with you. In my opinion the footprint of it would have left space for a small heatsink, laying down on the PCB, as many other projects ive done. Makes a huge difference, specially for higher loads.
But ill guess it was a chase of cutting expenses, by making concessions.

Reference for the voltage regulator
Im gonna assume the shield u mentioned is also using a 5v rail out of Arduino right ? or the 3.3v?

U said almost untouchable, so that means wont be too bad ?!?
If u powering with it a 9V standard wall power adaptor(normally they go up to 1 A/900mA) n, shouldnt be from there.
id say 68C seems quite within reason, considering has no heatsink.

The AMS1117 series of adjustable and fixed regulators are easy to
use and are protected against short circuit and thermal overloads.
Thermal protection circuitry will shut-down the regulator should
the junction temperature exceed 165°C at the sense point.

The power dissipation of the AMS1117 is equal to:

PD = ( VIN - VOUT )( IOUT )

Maximum junction temperature will be equal to:

TJ = TA(MAX) + PD(Thermal Resistance (junction-to-ambient))

Maximum junction temperature must not exceed 125°C.

and
Thermal Resistance
Control Section -40°C to 125°C SO-8 package j JA= 160°C/W
Power Transistor -40°C to 125°C TO-252 package j JA= 80°C/W
Storage temperature - 65°C to +150°C SOT-223 package j JA= 90°C/W*
* With package soldering to copper area over backside
ground plane or internal power plane j JA can vary from
46°C/W to >90°C/W depending on mounting technique and
the size of the copper area.

Thermal Considerations
The AMS1117 series have internal power and thermal limiting
circuitry designed to protect the device under overload conditions.
However maximum junction temperature ratings of 125°C should
not be exceeded under continuous normal load conditions.
Careful consideration must be given to all sources of thermal
resistance from junction to ambient. For the surface mount
package SOT-223 additional heat sources mounted near the device
must be considered. The heat dissipation capability of the PC
board and its copper traces is used as a heat sink for the device.
The thermal resistance from the junction to the tab for the
AMS1117 is 15°C/W. Thermal resistance from tab to ambient can
be as low as 30°C/W.

Im gonna assume the shield u mentioned is also using a 5v rail out of Arduino right ? or the 3.3v?

what about checking the datasheet of the mentioned regulators and see their normal temperatures ( with and without heatsink?!?)
That way you will start getting used to reading a datasheet.

Thinking about it, still has quite a bit of work involved, mind. and will still need to be around the time signature. OK-ish for simple basic ones( 2/4,4/4, etc) quite more complicated to complex ones. Maybe best way is design an embeded metronome with a led, to solve the time issue.
as quantizing goes, you have to think about the division of the tempo, and you know how auto quantizing is prone to mistakes(live aint a good thing), So id probably just stick with the arpegiator side of it. what synth you have?!? Most can do quantizing themselves
Wouldnt it be much easier to define the tempo on the synth, and maybe have the arduino read the MTC ?!?!
http://www.sparkfun.com/products/9595 maybe you can start with this for your tests and exxperiment/dev of the code, etc

AHHHHHHHHHH We finally got somewhere ! lol
yeah, that seems much easier.

No, thats not what u asked for. U asked a way to  record, loop, quantize, transpose if requested, etc... A bit like the some cheap instructional keyboards do, like transposing it depending on what note u chose, and according to a scale...Is that it ?

Ah, wait- Are u refering to an arpegiator instead ?!? Cause that is what the video sounds like, each note triggered and the arpegiated to a time signature. If so, thats a whole kettle of fish.

Even the old sequencers had a time signature(Ex a decade counter or other means)

You havent got the main issue/obstacle here... THE TIME SIGNATURE NEEDED for arduino know where to end the loop.Unless you make it in the arduino, use it to record those notes, and only then he can [process, quantize, and if requested change pitch( aka transpose), or increase/deecrease tempo.. Only that way would work just with arduino.

Where im getting is that is not as simple as you think it is... And cubase has come a long way. Maybe you need to catch up with all its new features. A lot of [people gave up on their 20 grand mixers and dozens of thousands of pounds just to trade it for a more digital based one. I still keep my fully analog based studio with a 48 channel mixer and 24 multitrack recorder just cause i love the analog stuff, plus im a dub head, otherwise i can tell u i would have done the same. I also have 20 channels in and 20 out of cubase( as a back up thing and for more digital genres, as i also compose for many artists) and know cubbase quite well.. What you saying, even live is so easy, with it. If you knew how hard it is to match  a loop to a live performance, you would give up now or at least understand what im saying.
Now if you wanna do it for proof of concept, you will definitely need more than just an  arduino, i can tell u that now !! Hands down !!
Sit down, do a block diagram of all things and how they will work ( might be easier to understand), and you will start realizing what im saying !!
without a time signature, there is no loop. At least not a workable one, as would be all over the place.
Record something, or use a live band track, and try to make a loop out of it....and note the time and how hard will be to do so !! Then let us know