So i just want to tell you that i've done successful rewrites!
The biggest was rewriting the e-commerce site of a well-known toy company. They had a homegrown site written in .NET, and we rewrote it on top of a commercial e-commerce framework in Java. It took a couple of years, the rewrite team was 2-5 times the size of the team that built the old site, and the client ended up with all the features of the old site, plus internationalisation, plus thorough automated tests and deployment. They seemed to be really happy with it.
The smallest was a data-aggregation server my team uses. It was written in Node, and kept crashing under load. I rewrote it in Java. It was just me, and it took a week or two. It hasn't crashed since, and we've been able to add loads more features.
Success factors in both: putting effort into thoroughly understanding the old thing; resisting any temptation to add new features unless you are exceptionally confident in how much more work it will take; thoroughly testing what you build as you go.