Getting a long-term visa in Singapore is very, very difficult, unless you have a local job - which is also difficult to get! Given the situation, a "visa run" like in Thailand with a short trip to a neighboring country and immediate return also seems questionable. Immigration is likely to question you upon return (based on experiences of people who've tried in normal times).
While I'd expect the SG government to be reasonable under the circumstances, I wouldn't expect "I like it here better than at home" to qualify for a visa. Let's hope that the situation improves in the next 90 days...