What fun is that?
While I'd be tempted in our machines to go full depth with a 3/8" tool, I know what kind of coolant flow I have with the flood coolant; I don't know how your coolant flow is.
And since you sound like you're okay with it nibbling away and taking a couple minutes longer than technically possible, I'd use a 3/8 tool down the middle in 2, maybe 3 passes just to be "safe". You want to avoid chips getting packed in the flutes. They can, and will, weld into the flutes if you don't have enough coolant to flush them out.
with a 3/8" tool going 5000rpm, lets say a 3 fluter (2 would be good, 4 is too many but you can use it) you could go about 30" inches per minute (about 80mm/min, 55mm/min for a 2 fluter) for the full slot down the middle (taking 2 or 3 passes of course) and that would be conservative
after going full slot down the middle, step out to finish the walls the last little bit at a bit faster feeds.
Some would say that's too slow, and they might be right, but it will work, and you probably won't break any provided your workholding is good and you have good coolant.
Just thought as I walked away, if you do want to go *a bit faster*, 1 minute saved on a 300pc job is 5 hours of cutting time. You could save a day of work just pushing this one tool a bit faster. Up to you.
And if Tom chimes in about how trying to save one minute of cycle time can cause 10 hours of fixing the machine, and how he has spent hours removing broken drills 10" deep into his 10000$ parts...
. I get 1/3 in^3/min. We can do better 
.
