It's too early for me to say about my daylilies, but I lost quite a few iris buds due to bud rot from all the rain. I wouldn't be surprised if this is true for daylilies too. We've broken rain records here (central NY) for June. It's also been colder than usual for the most part. Keeping my fingers crossed for better, warmer weather.

Hoping someone with more experience can help you out with more questions.

You can use scissors to cut the blooms near the bottom which would reduce weight. I'd leave about 1.5" of spent bloom still attached. I hope this works. It has for me.

Nancy

Yes, cut the spent flower off just above the ovary. Otherwise, the goop from the spent flower will get on your cross tags. It will also lessen the chance of pulling the forming pod off.
If you have cool weather and rain, those conditions are usually more conducive to pod set with tets. I suggest using a good fertile pollen to set a pod. Then come back with the cross pollen you want. You can also use a dip on the tet. The dip pollen tubes are thinner than the tets and you will usually get a pod from them which will fall off in a few weeks, but the plant will get into the mothering mood and be more likely to set pods.
Lastly, check both plants ploidy. I have tried crosses and later realized I was trying to put tet on dip, which of course didn't work! Also, be sure not to try crossing plants that are not established well, as it is not healthy for the plant.
Good luck, Ed

Cutting the dead blooms is a good idea.
Does anyone know how soon it is safe to do so?

You can cut them the following day. Pollination usually occurs within a half-hour.

Nancy

This has been very helpful! Thanks!