Go for the SmallRig Bottom Mount Plate for Sony Alpha 7C II / 7CR setup! I love mine because that Arca-Swiss plate is so handy for travel.

• SmallRig: Amazing value and feels super solid.
• Sony GP-X2: Looks nice but way too pricey tbh. Grab the Peak Design Slide Lite Camera Strap too. A wrist strap for 10 miles? Your hand will totally hate you lol!

I actually started out with the Sony GP-X2 Grip Extension because I’m a sucker for official gear, but I ended up feeling a bit let down. It looks amazing, no doubt, but the lack of an Arca-Swiss plate meant I was constantly fumbling with tripod plates in the middle of Tokyo. It felt like I paid a premium just for a logo and not much else. Instead of a bottom plate, have you looked at the SmallRig Thumb Grip for Sony Alpha 7C II / 7CR? I found that once my thumb had a solid place to rest on top, I didn't actually mind my pinky hanging off the bottom as much. It changes the whole balance of the camera in your hand and makes it feel way more secure than just adding height at the bottom. For the strap, the Slide Lite is fine, but it’s kinda bulky for such a small body. I much prefer the Peak Design Leash Camera Strap. It’s way thinner and honestly more comfortable for long days because it doesn't have that stiff seatbelt padding that digs in. I also usually keep a Peak Design Cuff Camera Wrist Strap in my pocket for when I'm in crowded areas and want the camera tucked safely in my palm. TL;DR: Forget the expensive Sony grip. Get a thumb grip and the PD Leash. It’s a much more agile setup for travel and stays well under your $150 limit.

Been thinking about your kit... I've been really satisfied with this alternative combo for travel:

• Neewer L-Shape Handle Grip for Sony a7C II : Honestly feels great and has that Arca-Swiss base for way less cash.
• BlackRapid Cross Shot Breathe Camera Strap : This is a lifesaver for those 10-mile days because it wont strain your neck like a standard strap. This setup works well and keeps you way under your budget!