These C4 respirators have been around for about 20 yrs, and I've never had a problem with the straw thingo. Here we use the UK S10, same style of straw too, and never an issue.
I guess practice makes perfect, try differnt methods of getting the straw, and go from there. Then whatever works for you.
Face it you won't be using the mask much once that phase of training is over.
In all my years in with the NBCD/NBCW/CBR thing, aside from the odd visit to the gas hut, only the last 6 weeks of my tour in Iraq did we carry the masks outside the wire for real, and that was do to huge enemy chlorine (pressurised in about 9kg sized bottles) bombs used in jam packed cement/dump trucks, along with a nasty HME booster. One day in Baghdad, one was SVBIED'd, killing about 7 and causing gas casualties of over 300. I think I was the first of my family to carry a mask from a genuine gas threat since my Great Uncles in 1916-1918 in Europe.
Regards,
OWDU