From the facts stated by you, your case appears to have become stronger because the issue is no longer merely one of delay in completion. According to your latest clarification, the company has not even commenced the work and has repeatedly postponed taking a final decision despite having accepted approximately ₹6,00,000 from you and having represented that the project would be completed within a specified timeline. Their subsequent communication that they are unable to undertake the project on an end-to-end basis, despite having accepted the assignment on that basis, may amount to a deficiency in service and breach of contractual obligations under the Consumer Protection Act, 2019.
In these circumstances, you should not remain indefinitely bound by their repeated assurances of "one more day" or "we will update you tomorrow." Before engaging another contractor, it would be prudent to send one final written communication by email clearly recording the entire sequence of events, referring to their repeated commitments, the fact that no work has commenced, the prejudice caused to you due to your commitment to vacate your rented premises, and calling upon them to confirm within a reasonable period (for example, 48 to 72 hours) whether they will immediately commence and complete the work as agreed. The communication should also state that if they fail to provide a firm commitment or commence the work within the stipulated period, you shall be constrained to engage another contractor at their risk and cost, without prejudice to your right to claim compensation, additional expenses, and other consequential losses.
If they still fail to respond or continue postponing their decision, you would be justified in engaging another contractor to avoid further loss and hardship. Doing so should not, by itself, weaken your legal claim, particularly where you have acted reasonably to mitigate your losses. In fact, consumer fora generally expect an aggrieved consumer to take reasonable steps to minimise the damage rather than allow losses to accumulate. However, you should preserve all documentary evidence, including the agreement, payment receipts, WhatsApp messages, emails, photographs of the site, quotations from the new contractor, invoices, and records showing the additional expenditure incurred due to the original company's default.
The company's repeated failure to provide a final decision, despite multiple follow-ups over several days, coupled with its refusal to honour the agreed scope of work and repeated postponement of the completion schedule, would certainly support your contention that there has been a continuing deficiency in service and unfair conduct causing inconvenience, financial loss, and mental harassment.
After issuing the final written notice and allowing a reasonable opportunity to respond, if there is still no satisfactory action from their side, you may proceed with another contractor and thereafter initiate proceedings before the appropriate Consumer Commission seeking compensation for the additional costs incurred, delay, mental harassment, and any other losses that can be substantiated by evidence. This course of action strikes an appropriate balance between protecting your legal rights and ensuring that you are able to move into your apartment without suffering further avoidable delays.