i have a very similar situation with a client. An unstable 6x6 timber wall, 6 feet tall, sloping backfill at 25% grade, built without a permit.
'Chance anchors' are soil nails which is mechanically stabilized earth (MSE) system. Embedment depth about 8' and spacing 2 rows at 4 feet, $300 - $500 per, plus strengthening of wall face. I don't have confidence in the longevity of the helical steel plate anchors.
Deadman anchors (tiebacks) need to be grouted to full bond length beyond the slope failure plane, about 15 feet or more, specialty equipment required, local company (Virginia) JES does a lot of these for basement walls, cost about $1000 per, spacing 2 rows at 8 feet. Load testing required, long term creep is a problem in soft cohesive soils.
I considered concrete buttresses in front of the wall. this saves some concrete material but the 'reverse cantilever' footing still needs to be continuous along length of wall and reqiures more width than a regular cantilevered footing under the wall.
I'm currently considering simply grading for a sloped embankment, no wall, but we may not have adequate room.
Also am looking at a wood 'crib' wall which will salvage a lot of the existing wood material. The crib wall design is another form of the MSE system seen with geogrids and soil nails.
HTH,
David