What I would do.
First check the slope itself is stable longterm. For loads on the anchor points the first thing is to ascertain the safety factor without any supplementary support to friction, and counting the vertical loadings imparted from the surface (consider also cases with the wedge of earth above and its weight laying on the pipe). If it stisfactory enough this way, you need not any supplemental block.
In other case you may decide impart the difference in inclined force to get your wanted safety factor from the concrete blocks. Counting the overall inclined resulting force from the whole weight should be overconservative and I think it unnecessary.
A 1.5 safety factor minimum should be provided in total for this a sliding situation; maybe even more given that the flowing water will impart some dynamical movement to pipes and fixity points, under pressure pipes try like long balloons for the children to straighten corners.
Then, you may try to extract resistance either from footings or piles. Respect the first case you have the resistance of footings with inclined piles; you may find them stated in Bowles. Only the part of vertical weight not accounted in getting the safety factor along the pipe could theoretically be counted at the footings; better not; hence if you have spent all in deriving a safety factor without the blocks to add against sliding, you will have only a horizontal force on a footing, for the differential as to get say an 1.5 safety factor, that you need deal with either with friction or passive push.
You may deal with this with piles and passive push reaction on them. Essentially if as in the previous case you have determined your horizontal force that way, you have a pile with a horizontal force atop embedded in a slope. You may dismiss part of the superficial depth in this, and for the passive push coefficients, use the proper formulations accounting for the unfavourable disposition of the slope (Caquot-Kérisel, graphically within limits, or some stated for the situation).
Examine as well how the nature of the soil and the presence of the water affect your design. You may need to count on diminished standing friction or just count on the adhesion-friction available for the wedge if a cut in clay.
Put extra blocks atop and at bottom.
What above for a straight section along the slope and pipe. If the pipe goes skewed along the slope, modify the reasoning above accordingly.