Is it permissible for someone in a state of major ritual impurity (janabah) to perform tayammum if they are unable to perform ghusl due to lack of time and social impediments?

If it is possible to go to a house or another place to perform ghusl (definition) before the prayer time expires, then it is obligatory to do so, even if it requires paying a customary fee, provided one can afford it. However, if ghusl is not possible due to lack of water or fear of harm from using it (such as extreme cold with no possibility of heating the water), then tayammum (definition) is permissible, and according to the soundest opinion, there is no need for repetition. But if no place for ghusl can be found after exerting effort, and there is fear that the prayer time will expire, then tayammum for prayer is permissible.