Sleeper retaining wall

I am building a retaining wall of new oak sleepers. The sleepers are 2400x200x100mm and are lying on their 200mm side. I have stacked 4-6 on top of each other (staggered the joints of course). I fixed them to each other with 150mm stainless steel timberlock screws (at least 6 per 2400mm sleeper). On the top course of sleepers I would like to hide the screws more than by just countersinking the heads. I was planning on countersinking the head deeply and covering them with a short oak dowel plug (see schematic drawing attached). My question to you guys is, how deep would you make the hole for the 18mm diameter dowel plugs? I would like to have them just as deep as necessary, because drilling the 18mm holes will be quite some work...
Please let me know what you think!
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I don't think your 'plug' covers need to be more than 1 or 2 cm at most. As said - they're aesthetic only. Just make sure they're in tight, so that no glue is needed, in case you need to access the screws in future.
I live in west central Scotland - not where that photo is...