Refactor ProcessGetData in anticipation of avoiding cs_main for ABC

Summary:
This is a refactor only, no functional change.
Partial backport of core PR11824 (commit 66aa1d5)

Depends on D2605 and D2620

Test Plan:

make check
./test/functional/test_runner.py

Reviewers: #bitcoin_abc, deadalnix, jasonbcox

Reviewed By: #bitcoin_abc, deadalnix, jasonbcox

Subscribers: jasonbcox, teamcity, schancel

Differential Revision: https://reviews.bitcoinabc.org/D2606