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Looking for advice on the best approach for modelling juvenile turtle survival in population where headstarted turtles are released every year. I am looking to use r-MARK.

We have radiotelemetry data and some opportunistic sighting and trapping data:
-For radiotelemetry, turtles are typically tracked weekly from May to October. Turtles can be confirmed alive, dead, or status may be unknown (either the turtle was pinpointed within ~3m but not seen, or a signal on the turtle could not be detected by radiotelemetry). We do have a number of cases where transmitters have fallen off. Typically, we try to capture turtles once a month and so status is likely confirmed within this timeframe. In November and April, turtles are tracked ~bi-weekly and from December to March, turtles are tracked about once a month, but the status is always unknown (turtles are brumating). We could assume survival probability would change over the course of the year, with turtles being most vulnerable when they are first released and likely remaining alive through the winter once they are brumating.
-If we see a turtle while we are in the field for radiotelemetry or trapping surveys, we will capture and record the sighting.
-Trapping efforts have occurred in some years but this has varied across years.
-Every year, new individuals are added to the population.
-Emigration from the study area is unlikely.

Any advice on best methods for what type of model would be most appropriate for these data are much appreciated!

If I'm understanding correctly, the problem is that you have multiple methods of detecting the turtles: radio telemetry, physical capture, and sightings. One way you could handle this is by treating the experiment as a robust design.

The robust design combines both open and closed mark-recapture models. Detections occur over a series of secondary occasions which are grouped into primary periods. Animals are allowed to come and go between the primary periods, but the population is assumed to be closed within primary periods. Usually, the primary periods are based on time. E.g., you might capture animals for 5 consecutive days every month. The robust design would assume that the population is closed over each 5 day period, but allow for animals to come and go from one month to the next.

In your case, you could break the experiment into, say, weekly primary periods and treat the different methods of capture as the secondary occasions. Each week, you would have three secondary occasions (i.e., three entries in the capture history) indicating whether or not the individual was detected with each of the different methods. You could then model the survival on a weekly basis. 

There are some caveats to this approach. The standard robust design will assume that the different methods of detection are independent. I.e., whether or not an individual is detected with radio-telemetry doesn't affect whether it is sighted or captured physically in the same week. This is probably not true, but it may be close enough depending on the capture probabilities. It also means that you have to include all detections in the data. I.e., you need to make sure to include any sightings even if the same turtle was detected with radio telemetry, or else you will introduce negative dependence. The standard model also will not account for any spatial information. Whether this is important will depend on how well the turtles move within the study site. If individuals tend stay within certain areas, then this could bias the detection. However, including this would make the models more complicated.

There is an example of how to fit the robust design in the RMark package (robust: Robust design example data in RMark: R Code for Mark Analysis). I'd also recommend reading Chapter 16 of Evan Cooch's  Program MARK: A Gentle Introduction.