You are working with a slope. Grass on that slope will look different than the grass above on the flat area. What plants did you take out? From what little I can see, that slope should be planted with a low shrub that will fill that space in without having to regrade, fill and redo the irrigation entirely.
If you do decide to plant grass you will have to grade, compact, possibly top dress and roll again lay the sod (horizontal to the slope)and either before or after your sod installation you will have to add another zone of irrigation heads to your irrigation system...you'll have to set the timer for lots of short soakings instead of just one per day. So if this is say, zone 8, you would set zone 1 to go off for 10 or 15 minutes or what ever the plants in that zone need and then set the zone 8 to go for 5 minutes. Set zone 2 and then zone 8 again for 5 minutes. Zone 3 for whatever that zone needs and then do zone 8 again. You also will have to mow that zone. Kind of steep. How long is that slope and where does it go? Where does excess water go?
What system is it you have? How many zones? Drip will not work for your grass. Was your drip on a zone of its own?
If you were to plant...Lonicera pileata, Box Honeysuckle you could use that drip system. I'd just rake up that bank and plant this plant in your holes. #1 or 1 gallon plants would cost...$10 per plant as an average. Plant these 3' apart offset. Try not to make straight lines. Leave a few 'holes' to plant perennials or a specimen tree. In 2 years those plants would cover that area and be breath taking. No mowing btw. No pruning. Fragrant. Evergreen. Fine texture. Rich green to contrast with St. Augustine.
Lonicera pileata as an example
You should probably consider a barrier strip between the lawn and this bed. pt 2X4'scored to bend (or plastic dimensional lumber 2X4 such as Treks in dove gray, no scoring necessary), staked in place will stop St. Augustine from spreading into your bed of shrubs. The height of these shrubs is perfect to effectively shade out the soil beneath to prevent germination of most weeds.
This bed will need a good soaking and then allowed to dry out before watering again. Unlike your lawn. So it will not be watered of course every time you water your lawn. Perhaps at first when you've just planted until the plants become established but all plant beds should be handled differently than the lawn, different needs. Different watering times different types of fertilizer.