The easy answer is "no", your HP OEM board will never have a bios with enthusiast / overclocking / etc. options in it.
The longer answer is that there is a fair chance your board is essentially identical (or similar enough, mainly the chipset(s) and Super IO controller need to be the same) to another or multiple MSI retail boards. If it is, you may be able to force it to take the MSI retail board bios... but even then, that retail bios may or may not have *all* the oc/etc options you're looking for, but these days even mATX boards do tend to have more options than they used to.
Sometimes there are jumpers missing, you might need to solder in a jumper wire or cut a trace or soldered in jumper or add a pin header, etc. This is more likely the older a board is, more often on newer platforms it's all bios, no more hardware mods necessary (but I don't know what that board is like).
You might link a good picture of the board, or to further sources of info and look for the MSI retail equivalent models and report back on those. It need not have same # of PCI slots, or some other parameters... doesn't necessarily have to look identical to your board.
You listed two board model #s too, what's that mean?
The first, 7093, has a bios on MSI's site. Maybe the other does too (I didn't check). If your research finds these boards have same chipset, same SuperIO chip, are compatible "enough" in the functions you need, you might try to flash that bios.
DO SO AT YOUR OWN RISK!
I've flashed tons of OEM boards to retail bios, but not that board specifically and come to think of it, never an ATI chipset based board. Haven't flashed anything very recent though, usually I pick up these OEM boards after someone brings it to me and given the option of bench fees or replacement (upgrade), they go with an upgrade and I get the board- since I'd never buy an OEM system for exactly these kinds of limitations, especially when I end up with somebody's old system case, board, PSU and windows license for free and they get their choice of upgrade for lower cost... a win/win situation.
Anyway, try uniflash. If the EEPROM is socketed, you might Google for "hot swap bios chip" for description of how to pull out the original EEPROM, leaving it intact for easy reversion back to the OEM bios, and instead flashing the experimental bios to a different EEPROM - if you have a spare. The other alternative is one of those online bios flashing services where for about $15 they'll flash your choice of bios to an EEPROM and send it to you to swap in yourself... though I wouldn't tell them what you're trying to do as they may not want to deal with support for that, just tell them what bios.
If the EEPROM is soldered on, the risk is higher, only you can decide if it's worthwhile to try on this system your first time, if uniflash (what I'd try to flash it) will even work, support whatever EERPOM is on the board or the spare EEPROM you have (though it does have reasonable support).