For my 2.7 I am currently using heavily modified zenith 40 tin carbs. I have a set of weber ida3c carbs however I am in the process of rebuilding those.

My engine seems to be running fairly well except for when I stomp on the gas, the engine sputters. I seem to be getting way too much gas out of the accelerator pumps.

What is the proper procedure for adjusting the accelerator pumps? I know how to physically adjust them- I just don't know how to get them to spray the proper amount.

google it and it comes up with southgate or similar,he has the Zenith manual on that site.
While since I did mine and don't recall the setting,the pump noozles block up and cause a stumble or flat spot check to make sure they are all clear and spraying properly.
Strange has it always been like this or recent problem? your timing is set properly right?.

Sorry, I should have mentioned that this is a freshly rebuilt engine and also freshly rebuilt carbs.

Sorry put you wrong it is suggate.co.uk,google Porsche 911 Zenith carburetors it will come up.
The ventury size is important,my research indicated the 32mm will work for 2.5 to 2.7,some have used 34mm but I seem to remember that is with higher lift cams,if not will result in a flat spot till the RPM gets up...results in a soggy bottom end as they say .
Main jets will be around 140 and idles 55,good place to start,however don't know what your carb guy set up you up with.
It's about how you want the car to drive ,I research and do it again,and its about how the engine responds in the normal driving range that really matters,happy to receive comments from others ,we never stop learning eh.
Some will know more than me and happy to be corrected,cheers.
Good Luck