If your computer does not have a firewire port
or HDMI inputs, then selecting the HV40 will be a frustrating experience. HDV is preferred because of the compression technology and the high-speed nature of the things you want to capture. AVCHD-compression is not a good idea for fast motion.
Since we don't know what you are currently using and we don't know why it "can't go the distance" we are at a disadvantage - we can't see what you see.
We hope you are not looking for the type of slow motion playback seen at the World Series. The Phantom high speed cameras used during the broadcast are about 100x more than your budget. As well, if you want to "look pro" keep in mind that upwards of a dozen cameras are used at broadcast games (and those cameras are studio-grade, typically have no internal video recording or audio capability and send the video signal to a booth for processing and getting sent to viewers)...
Where the camcorder is placed, lighting and NOT capturing the video hand-held will all contribute to the quality of the end-product.
Personally, I don't think a *single* consumer-grade device is up to the task. Assuming the lighting is good, the device is used on a tripod or other steadying device and is placed in a half-decent area to capture the game, augment that edited, wide-shot, video with high-speed video from a GoPro Hero3 or other similar "action cam". You might need to add a zoom lens to the action cam as most are not designed to capture distant views up close.
If you still think your current camcorder "can't go the distance", then something like a Canon HF R400 or similarly priced camcorders from Panasonic, Sony or JVC should work just fine. Since the "wide angle" camera does not need to do everything, you don't spend the whole budget on it...
High level process:
Once the wide shot camera is placed, it does not move. The action cam will always be pointed at your ball player. Press record on both cameras. Clap. This gives you a marker for synchronizing when editing. Capture the video. Game ends. Press stop recording. Import the video to a multi-track video editor. Synch the video using the clap you did when you started recording. Cut the video from the high-speed cam you don't want. Save. Render to a low-compression, high quality, media file. This is the archive. Use a transcoder to compress the file to an MP4. It will still be too large for uploading. Standard definition DVDs can be made from this - assuming you have a DVD authoring application. You can also edit it as a separate project for only the highlights.
The camcorder is only part of a much larger system - and there are different process flows for the different types of video you want/need.