Road legal is not an concern no.
I have seen footage of a 1500w DD hub power it's way up a hill, so I know it's capable. But will they not suffer from other issues like overheating or struggle with the strain of constant hill climbs.
Yes, no and maybe.
I am a big fan of big rear-mounted DD hub motors. I love the simplicity, durability and reliability of them. Nothing else comes close in these aspects. Generally speaking, they can also handle far more power than most other types of motor.
Mid-drive motors will always be more efficient hill-climbers as they give the option of massive gear reduction, leaving you able to climb a hill of almost any gradient at a snail's pace. This doesn't necessarily translate into
faster hill-climbing, but they will always remain cool while performing in this manner. For extreme gradients, they will be the most reliable, but are not without their own issues.
My most used bike features a 1000W rated Crystalyte 3540 DD hub, driven at around 3000W. I recently tackled Wiltshire's highest peak (Milk Hill) with this bike and it performed beautifully, absolutely flying to the top. The motor was quite warm at the peak, but I am running a fairly sophisticated system through a Cycle Analyst with thermal-rollback that will automatically dial-down the power to keep the motor within a pre-specified temperature range. There's no way an off-the-shelf mid-drive motor would have got me up there quicker anyhow. This isn't a riding style suited to everyone though.
If you
are still considering a hub motor, you should take a look at this motor simulator to give you an insight on how a given system would handle:
http://www.ebikes.ca/tools/simulator.html
I'm not sure how far you like to take things, but as a DIY'er, you might also be interested in recent advances in DD motor cooling as detailed here:
http://www.ebikes.ca/statorade.html