Website fingerprinting (WF) attacks identify the websites visited over anonymized connections by analyzing patterns in network traffic flows, such as packet sizes, directions, or interval times using a machine learning classifier. Previous studies showed WF attacks achieve high classification accuracy. However, several issues call into question whether existing WF approaches are realizable in practice and thus motivate a re-exploration. Due to Tor's performance issues and resulting poor browsing experience, the vast majority of users opt for Virtual Private Networking (VPN) despite VPNs weaker privacy protections. Many other past assumptions are increasingly unrealistic as web technology advances. Our work addresses several key limitations of prior art. First, we introduce a new approach that classifies entire websites rather than individual web pages. Site-level classification uses traffic from all site components, including advertisements, multimedia, and single-page applications. Second, our Convolutional Neural Network (CNN) uses only the jitter and size of 500 contiguous packets from any point in a TCP stream, in contrast to prior work requiring heuristics to find page boundaries. Our seamless approach makes eavesdropper attack models realistic. Using traces from a controlled browser, we show our CNN matches observed traffic to a website with over 90% accuracy. We found the training traffic quality is critical as classification accuracy is significantly reduced when the training data lacks variability in network location, performance, and clients' computational capability. We enhanced the base CNN's efficacy using domain adaptation, allowing it to discount irrelevant features, such as network location. Lastly, we evaluate several defensive strategies against seamless WF attacks.