My assumption is that the Blues will not be able to afford Schenn as a UFA after 2021, and Armstrong well knows this. A top priority for him will be extending Pietrangelo. This reality is mitigated by the presence of Robert Thomas, Jordan Kyrou, and other forward prospects in the Blues' pipeline.
So Armstrong works a deal with the Oilers, who are very deep at center but desperately need forward depth to turn a borderline playoff team into a contender in the Pacific. Armstrong requires the Oilers to take on Jake Allen, with the Blues paying $4 of the $9.2M owed to Allen over the final two years of his deal. Mikko Koskinen is clearly the man now in Edmonton (just signed a 3 year $4.5M AAV extension), but Allen is a capable backup (in Edmonton's eyes) who can push Koskinen.
The Oilers are cramped by big contracts to starts McDavid and Draisaitl, but their plan is buy out Milan Lucic soon and sign Schenn to a long-term deal. This positions them to better withstand the likely departure of Hopkins after 2021.
The Blues get youth in return. Jesse Puljujarvi, a big, fast Swede who has stalled in Edmonton and now wants out, joins the Blues. The Blues also get another big forward, Jujhar Khaira, to add to their mix of forecheckers. The Blues also get a conditional draft pick that becomes a second round pick if the Oilers extend Schenn before he reaches UFA.