Congrats on the GH6, it is a beast of a camera. Honestly, I have shot dozens of weddings and the most important thing is having gear that works when you are stressed and tired. You dont want to be messing with menus or checking if a mic is on when the bride starts walking down the aisle. I would skip the Panasonic DMW-XLR1 XLR Microphone Adapter for now. It is heavy, expensive, and honestly just adds another failure point if you are not used to XLR workflows yet. The GH6 preamps are actually pretty clean compared to older models. In my experience, these are your best options for staying under budget and keeping things light:

• Rode VideoMic Pro+ On-Camera Shotgun Microphone is the safest choice because of that auto-power feature. I have left mics off before and it is a nightmare you wont forget.
• Definitely buy the Rode WS11 Deluxe Wind Shield for it. The stock foam is useless in a real Seattle breeze near the water.
• If you want better audio quality, the Sennheiser+MKE+600+Shotgun+Microphone&linkCode=osi&tag=7649-20" target="_blank" rel="nofollow sponsored">Sennheiser MKE 600 Shotgun Microphone is better but it is long. It can run on an internal AA battery so you can plug it straight into the 3.5mm jack with the right cable and skip the expensive adapter. Stick to a setup that keeps the weight down. Weddings are a marathon and by hour six you will hate a heavy rig. Just set your camera gain low, usually around -12dB, and let the mic do the work. It keeps the noise floor way cleaner.

Jumping in here because I've spent way too many hours testing signal-to-noise ratios on these Panasonic bodies. Look, the GH6 preamps are actually pretty solid compared to the older GH4 days, but the trick is gain staging. Most people crank the camera gain and then wonder why they hear a hiss. In my experience, you want a mic with its own dedicated gain control so you can keep the camera's internal levels at the absolute minimum (usually -12dB or lower). Since you're worried about the Seattle wind and the weight of a massive rig, I'd skip the big shotgun mics for now and look at the Deity V-Mic D3 Pro Super-Cardioid Shotgun Microphone. It has a stepless analog gain knob on the back which is basically a cheat code for Lumix users. You just dial the mic up and keep the camera down. Plus, it has an internal battery that lasts like 50 hours, so a 8-hour wedding is nothing. If you're looking for deep dives on this, check out Curtis Judd on YouTube or his site... he's the absolute gold standard for technical audio specs and has saved me tons of headaches over the years. Also, if you're doing weddings, you really need a backup for the ceremony audio that isn't dependent on a wireless signal. I'd grab a Tascam DR-10L Digital Audio Recorder with Lavalier Mic. You tuck it in the groom's pocket and it records a safety track at -6dB automatically. If the wind kicks up or the wireless drops out, that little Tascam will save your career. It fits perfectly in your budget too even if you get both!

Can vouch for this

Will you be miking the groom directly? I've been super satisfied with the Rode Wireless GO II Dual Channel System lately because it's way cheaper than that adapter and saved my butt before.

Adding my two cents here as someone whos been through the ringer with audio gear over the years. I used to think I needed the most expensive, complex setup possible to look professional... until it failed me. I had a cable die during a vow exchange once and spent the rest of the night sweating bullets. Tbh, it taught me that reliability is king, especially for weddings where you dont get a second take. My current setup is way simpler than what I started with... I realized that for run-and-gun work, having a mic that integrates seamlessly with the camera without needing a massive adapter is usually the move. I focus on gear that has its own internal battery and a physical safety track if possible. It saves so much stress. Ngl, I still double-check my levels every ten minutes, but having a setup that stays out of my way lets me focus on the actual filming. If I were you, I would prioritize something lightweight that powers itself on and off. Youll thank yourself when youre eight hours deep into a wedding day and your wrists arent screaming at you.