Accounting problems generally use accounting solutions. The costs and hassle associated should be proportional to the costs needing to be allocated. Assuming the amount involved are unlikely to be material*, a good enough solution might be to simply apportion based on the number of persons likely to use the labs. This might actually make more sense than detailed usage tracking:
The "big ticket" items are presumably in heavy use and you can imagine a direct correlation (cause & effect, even) between usage and cost. In other words there is something approximating a "cost driver".
More general facilities, particularly if there isn't really "consumables" as such and taking hints from the posting that they are not near maximum capacity (no booking system), users generally benefit from the existence of the facilities rather than being proportionate to their use, there probably isn't a direct relationship between usage and costs. This is therefore more like overhead recovery and you're looking to apportion it using the most relevant method.
* It does occur to me that if this is a university budget every penny is fought over ridiculously so you might have a bit of a fight from anyone who thinks they are "losing out" (read: not winning) from any potential alternate approach. However this is true regardless of approach taken.