Hi,
I have not tried using WinHTTrack. But on command line I get a result showing
the pages locally you mentioned are missing in your HTTrack copy.

Here is the command used and which led to successful result:
(note: I interrupted the process as soon as I saw the webpage in question
working, as I don't want to wait until the whole website has finished, which
apparently takes some time)

---
httrack <https://www.songsimian.com/> -v -s0 -F "Mozilla/5.0 (Windows NT 10.0;
Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/74.0.3729.169
Safari/537.36" -%c2 -%B -%s -%v -A0 
---

Differences to your WinHTTrack config are actually not big.
Perhaps you want to adjust the following and try running it again:

1. remove the filters you set; I don't see a need of including them when the
initial website passed covers them already:
So remove these:
+www.songsimian.com*
+*.index.html

2. I did not set any language restriction. You may want to remove this setting
as well.

3. Browser ID: since you have not set any, HTTrack likely will use its own
one. Since HTTrack identifies itself as httrack, there might be some websites
identifying this information and behave differently. I found it mostly useful
to set this to a standard "real" browser identity in all cases so far. So you
may want to set it to for example a Chrome browser user agent.