From what I understand, this bottle wall would be indoors without risk of freezing? My following thoughts are based on this assumption.
I would use a large wine rack to support the bottles, as long as it is on a solid foundation, it will be designed to support the weight of full wine bottles. I would probably try to recap them with cork as this would help account for any expansion/contraction issues. If there is a freezing risk I would fill them with alcohol (concentration depending on low temperature risk), this will also address the algae issue. Depending on your local laws you may be able to make the alcohol yourself, or use diluted rubbing alcohol if that's not an option. If the risk of freezing is reasonably low, you can start with water and slowly work on replacing it with alcohol over time. If the risk is higher, then you could keep the bottles empty during high risk times.
