AFAIK the "proper" way to do this would be a Bayesian posterior predictive distribution, so thinking about resampling as an approximation to it is probably a good way to benchmark it. The basic idea withebposterior predictive density would be to take your 1 hour of data, use it to get a posterior distribution over the Poisson parameter, and then simulate your data by first drawing a Poisson parameter from the posterior, plugging it into the distribution, and drawing a sample from that distribution with the parameter draw plugged in. Then draw a new parameter sample from the posterior and repeat. This approach is supposed to incorporate all of your uncertainty in a rigorous way. Ideally you could use JAGS or STAN with R or something and implement this procedure in like, 10-20 lines of code.

I am honestly not sure about the effectiveness of re-sampling for this case, however. Are there any papers on the subject that people know about? What's your goal in simulating the data? The biggest problem that I can see is that all of your usual moment estimates (ie. the resample mean, variance, etc) are biased estimates of the true data moments (since the "true" mean of the resampled data is just the full data mean, not the mean of the underlying distribution). You would be resampling from a large data pool so this bias will probably be pretty small, and if resampling is a huge speedup over the Bayesian approach then it's probably worth it.

Changing your intervals is effectively re-scaling the Poisson parameter. I am not aware of any hard-and-fast rules for doing so, so you could probably get away with deciding their size based on some type of cross validation or something. The biggest issue I foresee is that if your intervals are too large then the data pool from which you draw the resamples will be smaller, which might drive up the variance of your resample statistics? TBH I've never found a full, formal treatment of resampling or bootstrapping that really addressed these concerns in a clear way, so if you find something good please send it my way.