HP Compaq Pro 4300 (IPISB-IK + i5-3330s?)

[sundog]

Hi everyone, thank you for keeping a forum like this alive and active!
I have more than a dozen HP Compaq Pro 4300 All-in-one machines that I'm going to be upgrading. Out of the factory, HP only offers support for 65W CPUs (These ones are all running the i3-2120, which I'm now looking to replace), and having tried a 95W i5-2400, the machine gave me a predictable "ERROR: Unsupported CPU installed. PC will automatically power down in a few seconds."

Mostly expecting this, since online benchmarks only show verified runs using other 65W CPUs supported by H61, some in the official HP supported list (i5-3470s, i7-3770s) and some not in the official list (i5-2500s), I have chosen to buy two CPUs to try in this unit, which are almost identical, and are the cheapest quad cores, comparable to the i5-2400 in performance, but limited to 65W: the i5-2500s, and the i5-3330s. 
The question here, is whether or not the machine will boot with the 3330s installed, since it's not on HP's supported list of CPUs (even though it's bigger brother, the i5-3470s is). I bought a 2500s as well, as backup, to use if it fails to boot, but this isn't the preferred option, as the 3330s is not only faster, it has a bump in integrated graphics performance, and it allows the machines to take advantage of the 1600MHz ram that is already installed in them, which is currently being limited to 1333MHz by the i3-2120, and will also be limited to 1333MHz by the i5-2500s. 

The ideal here, is that I can put a 3330s in every machine, as well as more ram and an SSD, and they should work like new again. But if the CPUs are limited by a whitelist, rather than a blacklist, I'm not sure if the rather obscure 3330s, never sold in these machines, will be compatible or not.
Since it's only a matter of time until the packages arrive and I can test them out in person, I thought I would ask here for some advice, and perhaps, a version of the latest BIOS for these machines, with the CPU restrictions removed regardless. Though I don't plan to install any 95W CPUs and put the system's power delivery board at risk, having the option to disable the unsupported CPU message, in case it reports the 3330s as incompatible, would be excellent. I have specifically avoided updating these machines to the latest BIOS revision, and will only update them to 8.12 Rev A (one version behind the latest) if needed, to make this a little easier. 

Here is the relevant information I can think of for these machines:

Currently installed:

Manufacturer: HP
Model: Compaq Pro 4300 All-in-One PC
Motherboard: HP IPISB-IK
Chipset: Intel H61
BIOS Version: 7.01
CPU: i3-2120s
RAM: 1x 4GB 1600MHz (Running at 1333MHz)

Planned upgrade:

CPU: i5-3330s
RAM: 2x 4GB 1600MHz (Running at 1600MHz)

Full specifications: Link
Latest BIOS update: 8.13 Rev.A

CPUZ Screenshots:

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