I love and use very similar ideas as you, which reminds me I need more metal coat hangers.You can use just about any cleaning product (except Whink) to clean a bottle. Hydrochloric (muriatic) acid will not harm the glass. LimeAway is commonly used if you have limey deposits or iron deposits. If the glass is "sick," that is, decomposing, no cleaning product will remove the sickness.
What I have found generally useful is laundry bleach.
I fill a bottle with tepid tap-water to which I add a tiny amount of laundry detergent (because it is non-sudsing) and a dollup of laundry bleach. I let it soak for a few hours.
Whatever residue is left I remove with a home-made brush. I use a stiff wire coat-hanger for this purpose. I cut the hook portion away. I bend the smallest possible loop on one end of the wine and a large loop on the other. The larger loop will be the handle.
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I cut a lengthwise strip of scrubbing pad (a Scotch-Brite knockoff from the dollar store) wide enough to generously cover the small loop. I roll the strip of scrubbing pad around the small loop and secure it tightly with several wraps of thin copper wire. String or a rubber band could be substituted for the copper wire. The copper is too soft to scratch the glass, but is relatively impervious to chemicals.
If you wish to use a commercial bottle brush, try this. I affix a small patch (about the size of the brush diameter) of scrubbing pad to the tip of the brush using polyurethane cement (Plumbers Goop, Shoe Goop, etc.). This patch not only makes the brush more effective in corners and at the bottom of the bottle, it also cushions the tip of the wire brush from any "hammer effect" in manipulating the brush inside the bottle.