No one in here has reported on the stability of H2O2....
It is not a stable chemical. It wants to turn to water and 02. If you expose it to light, the light (even in your bathroom over the sink) has enough energy to cause the oxygen to break off and bond with another broken molecule. That is why it is in solid brown containers and not see-through. It also says do not shake, for the same reason.
Most likely, long term would consist of you having to add H202 every week. Why? If you read the study, H202 in lower levels acts like crack to a junkie with the beetles.
You might want to try mixing Oxyclean (sodium percarbonate) with dry pollen and placing it in a container which the SHBs can get into but the bees can't. Sodium percarbonate generates hydrogen peroxide on contact with water suggesting that once the SHBs ingest it with pollen they should receive a healthy dose directly to their gut.
That is a very good idea, with a few exceptions. First off, it will injure you and do the same to you if you get it on you and you sweat or inhale the dust.
I would recommend reading the MSDS on it: http://www.sciencelab.com/xMSDS-Sodium_percarbonate-9927598