The solution to getting Paypal's verify endpoint to work was to serialize JSON manually like so:

PaypalWebhookVerifierExample.cs

using System;
using System.IO;
using System.Net;
using System.Net.Http;
using System.Net.Http.Headers;
using System.Text;
using System.Threading.Tasks;
using Microsoft.AspNetCore.Authorization;
using Microsoft.AspNetCore.Http;
using Microsoft.AspNetCore.Mvc;
using Newtonsoft.Json;

namespace server.Payment
{
	public class PaymentController : Controller
	{

		private static readonly HttpClient client = new HttpClient();

		[HttpPost("api/checkout/webhook")]
		[AllowAnonymous]
		public async Task<IActionResult> HandleWebhook()
		{
			var json = await new StreamReader(HttpContext.Request.Body).ReadToEndAsync();
			var headers = HttpContext.Request.Headers;

			await VerifyEvent(json, headers);

			// handle etc...

			return Ok();
		}

		private async Task VerifyEvent(string json, IHeaderDictionary headerDictionary)
		{
			var bearerToken = await Authenticate();
			client.DefaultRequestHeaders.Authorization = new AuthenticationHeaderValue("Bearer", bearerToken);
			
			// !!IMPORTANT!!
			// Without this direct JSON serialization, PayPal WILL ALWAYS return verification_status = "FAILURE".
			// This is probably because the order of the fields are different and PayPal does not sort them. 
			var paypalVerifyRequestJsonString = $@"{{
				""transmission_id"": ""{headerDictionary["PAYPAL-TRANSMISSION-ID"][0]}"",
				""transmission_time"": ""{headerDictionary["PAYPAL-TRANSMISSION-TIME"][0]}"",
				""cert_url"": ""{headerDictionary["PAYPAL-CERT-URL"][0]}"",
				""auth_algo"": ""{headerDictionary["PAYPAL-AUTH-ALGO"][0]}"",
				""transmission_sig"": ""{headerDictionary["PAYPAL-TRANSMISSION-SIG"][0]}"",
				""webhook_id"": ""<get from paypal developer dashboard>"",
				""webhook_event"": {json}
				}}";
			var content = new StringContent(paypalVerifyRequestJsonString, Encoding.UTF8, "application/json");

			var resultResponse = await client.PostAsync("https://api-m.sandbox.paypal.com/v1/notifications/verify-webhook-signature", content);

			var responseBody = await resultResponse.Content.ReadAsStringAsync();

			var verifyWebhookResponse = JsonConvert.DeserializeObject<VerifyWebhookResponse>(responseBody);

			if (verifyWebhookResponse.verification_status != "SUCCESS")
			{
				throw new Exception("failed to verify webhook response");
			}
		}

		private async Task<string> Authenticate()
		{
			// TODO: make all hard coded values configurable
			var request = WebRequest.Create("https://api-m.sandbox.paypal.com/v1/oauth2/token");
			request.Method = "POST";
			request.ContentType = "application/x-www-form-urlencoded";
			request.Headers.Add("grant_type", "client_credentials");
			var postData = "grant_type=client_credentials";
			var byteArray = Encoding.UTF8.GetBytes(postData);

			var dataStream = request.GetRequestStream();
			dataStream.Write(byteArray, 0, byteArray.Length);
			dataStream.Close();

			request.ContentType = "application/x-www-form-urlencoded";
			request.ContentLength = byteArray.Length;

			var clientId = "<get from paypal developer dashboard>";
			var clientSecret = "<get from paypal developer dashboard>";
			var encoded = Convert.ToBase64String(Encoding.GetEncoding("ISO-8859-1")
				.GetBytes(clientId + ":" + clientSecret));

			request.Headers.Add("Authorization", "Basic " + encoded);

			try
			{
				var response = await request.GetResponseAsync();
				using (dataStream = response.GetResponseStream())
				{
					var reader = new StreamReader(dataStream);
					var responseFromServer = reader.ReadToEnd();
					Console.WriteLine(responseFromServer);
					var token = JsonConvert.DeserializeObject<TokenResponse>(responseFromServer);
					return token.access_token;
				}
			}
			catch (WebException e)
			{
				string content;
				using (var reader = new StreamReader(e.Response.GetResponseStream()))
				{
					content = reader.ReadToEnd();
					Console.WriteLine("content", content);
				}
				throw;
			}
		}
	}
}

Thanks for the detailed explanation. Unfortunately it is not working me! Always giving me FAILURE.