Jayeson asked: 316.2065 (5) has an exception for making left turns but not for continuing straight/avoiding right turn lanes. This would seem to imply that a cyclist must move into a right turn lane which would then require taking the right turn. A common example is where a narrow road widens and then forms two lanes at traffic lights, with one lane for right turns and one for straight through and left turns.
A cyclist continuing straight through an intersection is not legally permitted to use a lane marked for right or left turn only. See this post for the applicable statutes:
The statutes do not easily resolve all circumstances that we may encounter. Roadway design and construction does not always provide the optimum solutions for those circumstances. Such intersections present a dilemma for cyclists and each must balance compliance with the laws and the safest options.