What are my options for achieving a cold backup server for SQL Server Express instance running a single database?

I have an SQL Server 2008 Express instance in production that currently represents a single point of failure for my application. I have a second physical box sitting at the installation that is currently doing nothing. I want to somehow replicate my database in near real time (a little bit of data loss is acceptable) to the second box. The database is very small and resources are utilized very lightly.

In the case that the production server dies, I would manually reconfigure my application to point to the backup server instead.

Although Express doesn't support log shipping, I am thinking that I could manually script a poor man's version of it, where I use batch files to take the logs and copy them across the network and apply them to the second server at 5 minute intervals.

Does anyone have any advice on whether this is technically achievable, or if there is a better way to do what I am trying to do?

Note that I want to avoid having to pay for the full version of SQL Server and configure mirroring as I think it is an overkill for this application. I understand that other DB platforms may present suitable options (eg. a MySQL Cluster), but for the purposes of this discussion, let's assume we have to stick to SQL Server.