A Service, like a Drum– (line 6)
Percussion instruments are not normally associated with Christian Churches – at least not in the 19th century. The comparison of the service to a beating drum is pretty radical. It puts a very negative spin on the funeral. She doesn't distinguish between any of the specific parts of the service – they all blend together into one unpleasant rhythm.
And creak across my Soul With those same Boots of Lead, again, (lines 10-11)
Walking on someone's soul seems very disrespectful. It is ironic that the mourners at the funeral, who you'd think would be very somber and respectful, are the most oppressive figures in the poem. The religious community is an invasion on her private space and feelings.
Then Space–began to toll,
This line presents another (probably) negative view of an aspect of the church. "Space" is compared to a ringing church bell. At the end of a religious service in New England, it would be typical to ring the bell at the top of the pointy steeple. The sound crowds out everything else in this massive space.