The mirabait tool looks promising, and maybe you could get good results if you started with a wide enough net of possible mitochondrial sequences.

I would also suggest looking at read coverage as a way to separate these genome sources. It varies by species and cell type, but typically the mitochondrial genome has a much higher copy number than the nuclear genome. You could do a de novo assembly on all reads together, then try to stratify the contigs into your classes by their average read coverage. You could also attempt an assembly-free approach by doing this at the k-mer level.

There will be some ambiguity caused by repetitive regions, but you may be able to make progress with this approach. It has the advantage that it does not depend on finding accurate template/related mitochondrial sequences first, so if that task is hard or impossible, it may help. Conversely, if you can find good mitochondrial examples, I think the template approach will be hard to beat.

Assembly by Reduced Complexity will take a set of (annotated!) targets and produce unbiased assemblies. The paper is in review and available on bioarxiv. Our motivation for developing ARC was to do exactly what you want to do: assemble targets for which no close reference sequence is available. It's been great and extremely helpful for non-model genomic work.

FYI: I'm sure you're aware that (some?) chloroplasts have an inverted, duplicated region - assembling these regions are notoriously difficult, and it would make sense to mask one/both if the insert size of your libraries does not span it.