[Integration][JS] JS implementation is slow to build

### Describe the enhancement requested

The JavaScript build in the integration tests is a bit slow. Here on a 12-core CPU:
```console
# time /arrow/ci/scripts/js_build.sh /arrow /build
[...]

real 1m8.027s
user 8m26.377s
sys 0m55.688s
```

I don't understand much of what it is doing, but it _seems_ it may be compiling the TypeScript sources with several different compiler options and/or versions, and also linting the sources. Given that this is the Integration build, the build could probably be slimmed down.

### Component(s)

Continuous Integration, Integration, JavaScript