The Miracast works, but it is useless, because when it connects to a
mirrored display it also automatically switches off the regular WiFi, so
it is not possible to mirror streaming internet content, for example

I did a little research. Seems a lot of early/cheaper Miracast capable devices have the same failing, because they simply can’t handle the dual band wifi requirements. It’s not a bug, because the Ainol Novo8 (which uses the ATM7029) actually asks permission to turn off wifi, so it can connect to a miracast device. Rather makes the whole miracast thing pointless, imho.

My new Nexus 7 (2013) tablet works fine, with simultaneous wifi and miracast, confirming that this is a hardware shortcoming in the Ainol/Actions CPU

Is there anything I can do to speed the tablet up?

Sure. From the horse’s mouth (Actions themselves):
http://www.actions-semi.com/en/productview.aspx?cat=98&id=108
Note they explicitly state their SoC has VFPv4 support and an in-order pipeline. Well, a real Cortex-A9 has only VFPv3 but a superior out-of-order pipeline.

The ATM7029 was caught with a CPU ID (/proc/cpuinfo) of 0xc05, which is Cortex-A5. Then Actions updated the firmware and hid the ID. The CPU benchmarks (Vellamo Metal – forget Antutu, it’s crap) also point towards an A5.

For all the details, see here:
http://www.slatedroid.com/topic/44034-atm7029-an-arm-cortex-a9-or-a5/

Do you have a link to verify this?