After a point-in-time restore, is there any way I can get the transactions during restore time?
In Azure SQL DB today, the answer is "no" - at least not the way you are asking the question.  You can't go hack the log since it is a managed service and it (the log format) can change over time and thus is not exposed to you.  Instead, you can achieve the same end by setting up active geo-dr for the database.  You let it sync up and you can break the connection when you want so that you have an exact copy with all of the most recent transactions at the point where you want to have it.