Right now it is most likely KC who is holding up the trade, not Miami. Them picking a LT is a foreknown conclusion, so it isn't Miami who would gain leverage on draft day by the Chiefs selecting Joeckel or Fisher. The fact that they are trying to trade Albert reveals that. What gives KC the leverage are the OTHER TWO LTs.
Once Fisher/Joeckel and Lane Johnson are gone, demand for Albert will RISE.
SD would then join the Albert sweepstakes by offering their higher 2nd rounder for Albert completely taking the 54th pick out of the picture and forcing our 42nd pick.
Right now, the demand is only us because DET, ARI, BUF, and SD don't yet know for sure whether Lane Johnson will drop to them or not yet. Once Fisher/Joeckel are gone, Lane Johnson becomes the hottest commodity and then the teams left without that LT and need one badly ie SD and MIA now become the teams to offer KC their 2nd round picks for Branden Albert.
At this point, those who aren't blind bats can see that SD's 2nd round pick is pick 45. Only our 42nd pick would beat their offer eliminating the 54th pick from the scenario. Right now, if KC bites, we can get away with landing Albert for pick 54. Once the draft comes and Lane Johnson doesn't drop to SD, Albert becomes only available for the 42nd pick because SD's 45th beats out our 54th. Common sense why Ireland and Aponte want to do the trade NOW, not Thursday.