This music is not meant for large modern-day SATB choirs. The voicing is closer to STTB than SATB. An ideal ensemble for this music would be 8 singers – 5 male and 3 female, with the alto part shared by a high tenor and low alto. The ensemble should certainly be no larger than than 16-20 voices. It is advised to place half the altos on the tenor voice and half the tenors on the alto voice since these two voices are nearly identical in range and difficulty.
Pitch the music to match your ensemble. It is highly unlikely that neither the Imperial Hofkapelle, nor the Constance Kantorei used A-440 tuning. Most historical evidence indicates a much lower pitch. It can be extremely taxing for adult females (or boys) to maintain some of the soprano lines at modern pitch. A semi-tone lower makes sense (but a nightmare for any accompanist!).
My tempo suggestions are just that. However, whenever proportional signatures change, they are always in relation to the original tempo. Therefore, if the beginning indicates half note = mm. 60, and the next section is marked half note = mm. 90, then observe that relationship.
Performing the sequences with their missing verses (https://www.feiszli.net/choralis-constantinus/cc-music/) one has several options. Lacking a good organist (or organ), it is possible to sing the alternate verses as chant by a soloist or small group. For those sequences for which Buchner’s settings are available an organist can simply play those. For others a keyboardist with good improvisation skills can improvide on the chant or improvise while the singers sing the chant in long tones as outlined by Mary Berry (see the above referenced page). Instrumental doubling is also possible, assuming appropriate instruments are used since instruments were always part of the Imperial chapel. Reed organ stops and reed instruments are more likely to have been used than brass or strings.