https://www.sefaria.org/Tamid.31b.1?lang=bi&with=all&lang2=en
There is a very detailed description of how the animal is cut up, exactly how the kohanim are to hold it, and then all of the parts are then just set down on the ramp for the kohanim to say shema.
Why are the karbonos seemingly interupted for another mitzvah when if a person is already engaged in one mitzvah he is exempt from another (brachos 11a for example) so why stop the karbonos to say shema instead of reciting it after the tamid has been brought?
What is the purpose of this preparation if then the parts of the tamid are to be set on the ramp. Why would it matter how they are held and in what order?
At this point having been involved in shechita I would think they would not be wearing tefillin (not sure just a thought) so why would they be reciting shema seemingly without tefillin on?